Advertisements
Advertisements
Question
Solve the following:
Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.
A highway safety group is interested in studying the speed (km/hrs) of a car at a check point.
Advertisements
Solution
Let X = speed of the car in km/hr
Then X takes uncountable infinite values
∴ random variable X is continuous.
APPEARS IN
RELATED QUESTIONS
A random variable X has the following probability distribution:
then E(X)=....................
Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is hostler?
From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
An urn contains 25 balls of which 10 balls bear a mark ‘X’ and the remaining 15 bear a mark ‘Y’. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that
(i) all will bear ‘X’ mark.
(ii) not more than 2 will bear ‘Y’ mark.
(iii) at least one ball will bear ‘Y’ mark
(iv) the number of balls with ‘X’ mark and ‘Y’ mark will be equal.
A bag contains 4 red and 6 black balls. Three balls are drawn at random. Find the probability distribution of the number of red balls.
Two dice are thrown together and the number appearing on them noted. X denotes the sum of the two numbers. Assuming that all the 36 outcomes are equally likely, what is the probability distribution of X?
A class has 15 students whose ages are 14, 17, 15, 14, 21, 19, 20, 16, 18, 17, 20, 17, 16, 19 and 20 years respectively. One student is selected in such a manner that each has the same chance of being selected and the age X of the selected student is recorded. What is the probability distribution of the random variable X?
Find the probability distribution of the number of white balls drawn in a random draw of 3 balls without replacement, from a bag containing 4 white and 6 red balls
Two cards are drawn simultaneously from a well-shuffled deck of 52 cards. Find the probability distribution of the number of successes, when getting a spade is considered a success.
Let X represent the difference between the number of heads and the number of tails when a coin is tossed 6 times. What are the possible values of X?
Four balls are to be drawn without replacement from a box containing 8 red and 4 white balls. If X denotes the number of red balls drawn, then find the probability distribution of X.
Find the mean and standard deviation of each of the following probability distribution:
| xi : | −1 | 0 | 1 | 2 | 3 |
| pi : | 0.3 | 0.1 | 0.1 | 0.3 | 0.2 |
Find the mean and standard deviation of each of the following probability distribution :
| xi : | -3 | -1 | 0 | 1 | 3 |
| pi : | 0.05 | 0.45 | 0.20 | 0.25 | 0.05 |
Find the mean and standard deviation of each of the following probability distribution :
| xi : | 0 | 1 | 2 | 3 | 4 | 5 |
| pi : |
\[\frac{1}{6}\]
|
\[\frac{5}{18}\]
|
\[\frac{2}{9}\]
|
\[\frac{1}{6}\]
|
\[\frac{1}{9}\]
|
\[\frac{1}{18}\]
|
A fair coin is tossed four times. Let X denote the longest string of heads occurring. Find the probability distribution, mean and variance of X.
Two numbers are selected at random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X.
If the probability distribution of a random variable X is as given below:
Write the value of P (X ≤ 2).
| X = xi : | 1 | 2 | 3 | 4 |
| P (X = xi) : | c | 2c | 4c | 4c |
A random variable has the following probability distribution:
| X = xi : | 1 | 2 | 3 | 4 |
| P (X = xi) : | k | 2k | 3k | 4k |
Write the value of P (X ≥ 3).
A random variable X has the following probability distribution:
| X : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P (X) : | 0.15 | 0.23 | 0.12 | 0.10 | 0.20 | 0.08 | 0.07 | 0.05 |
For the events E = {X : X is a prime number}, F = {X : X < 4}, the probability P (E ∪ F) is
A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P (X = 3) = 2 P (X = 1) and P (X = 2) = 0.3, then P (X = 0) is
A random variable has the following probability distribution:
| X = xi : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P (X = xi) : | 0 | 2 p | 2 p | 3 p | p2 | 2 p2 | 7 p2 | 2 p |
The value of p is
If X is a random-variable with probability distribution as given below:
| X = xi : | 0 | 1 | 2 | 3 |
| P (X = xi) : | k | 3 k | 3 k | k |
The value of k and its variance are
From a lot of 15 bulbs which include 5 defective, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence, find the mean of the distribution.
Two fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution of X. Also find E(X).
If the demand function is D = 150 - p2 - 3p, find marginal revenue, average revenue and elasticity of demand for price p = 3.
The following data gives the marks of 20 students in mathematics (X) and statistics (Y) each out of 10, expressed as (x, y). construct ungrouped frequency distribution considering single number as a class :
(2, 7) (3, 8) (4, 9) (2, 8) (2, 8) (5, 6) (5 , 7) (4, 9) (3, 8) (4, 8) (2, 9) (3, 8) (4, 8) (5, 6) (4, 7) (4, 7) (4, 6 ) (5, 6) (5, 7 ) (4, 6 )
Find mean and standard deviation of the continuous random variable X whose p.d.f. is given by f(x) = 6x(1 - x);= (0); 0 < x < 1(otherwise)
Compute the age specific death rate for the following data :
| Age group (years) | Population (in thousands) | Number of deaths |
| Below 5 | 15 | 360 |
| 5-30 | 20 | 400 |
| Above 30 | 10 | 280 |
From the following data, find the crude death rates (C.D.R.) for Town I and Town II, and comment on the results :
| Age Group (in years) | Town I | Town II | ||
| Population | No. of deaths | Population | No. of deaths | |
| 0-10 | 1500 | 45 | 6000 | 150 |
| 10-25 | 5000 | 30 | 6000 | 40 |
| 25 - 45 | 3000 | 15 | 5000 | 20 |
| 45 & above | 500 | 22 | 3000 | 54 |
A sample of 4 bulbs is drawn at random with replacement from a lot of 30 bulbs which includes 6 defective bulbs. Find the probability distribution of the number of defective bulbs.
A die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of at least 3 successes
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Defects on plywood sheet occur at random with the average of one defect per 50 Sq.ft. Find the probability that such a sheet has no defect
Defects on plywood sheet occur at random with the average of one defect per 50 sq.ft. Find the probability that such a sheet has:
- no defect
- at least one defect
Use e−1 = 0.3678
State whether the following is True or False :
If r.v. X assumes the values 1, 2, 3, ……. 9 with equal probabilities, E(x) = 5.
Solve the following problem:
Following is the probability distribution of a r.v.X.
| X | – 3 | – 2 | –1 | 0 | 1 | 2 | 3 |
| P(X = x) | 0.05 | 0.1 | 0.15 | 0.20 | 0.25 | 0.15 | 0.1 |
Find the probability that X is odd.
Solve the following problem :
Find the probability of the number of successes in two tosses of a die, where success is defined as number greater than 4.
Solve the following problem :
The probability that a bomb will hit the target is 0.8. Find the probability that, out of 5 bombs, exactly 2 will miss the target.
Solve the following problem :
The probability that a machine will produce all bolts in a production run within the specification is 0.9. A sample of 3 machines is taken at random. Calculate the probability that all machines will produce all bolts in a production run within the specification.
Solve the following problem :
A computer installation has 3 terminals. The probability that any one terminal requires attention during a week is 0.1, independent of other terminals. Find the probabilities that 0
Solve the following problem :
It is observed that it rains on 10 days out of 30 days. Find the probability that it rains on exactly 3 days of a week.
Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as six appears on at least one die
A discrete random variable X has the probability distribution given as below:
| X | 0.5 | 1 | 1.5 | 2 |
| P(X) | k | k2 | 2k2 | k |
Find the value of k
Let X be a discrete random variable whose probability distribution is defined as follows:
P(X = x) = `{{:("k"(x + 1), "for" x = 1"," 2"," 3"," 4),(2"k"x, "for" x = 5"," 6"," 7),(0, "Otherwise"):}`
where k is a constant. Calculate Standard deviation of X.
The probability distribution of a discrete random variable X is given as under:
| X | 1 | 2 | 4 | 2A | 3A | 5A |
| P(X) | `1/2` | `1/5` | `3/25` | `1/10` | `1/25` | `1/25` |
Calculate: Variance of X
A random variable X has the following probability distribution:
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(x) | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
Find:
- k
- P(X < 3)
- P(X > 4)
