Advertisements
Advertisements
प्रश्न
Find the probability distribution of number of tails in the simultaneous tosses of three coins.
Advertisements
उत्तर
When three coins are tossed simultaneously, the sample space is
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let X represent the number of tails.
It can be seen that X can take the value of 0, 1, 2 or 3
P(X = 0) = P(HHH) = `1/8`
P(X = 1) = P(HHT) + P(HTH) + P(THH) =`1/8 +1/8+1/8 =3/8`
P(X = 2) = P(HTT) + P(THT) + P(TTH) =`1/8+1/8+1/8 = 3/8`
P(X = 3) = P(TTT) = `1/8`
Thus, the probability distribution is as follows.
| X | 0 | 1 | 2 | 3 |
| P(X) | `1/8` | `3/8` | `3/8` | `1/8` |
संबंधित प्रश्न
A random variable X has the following probability distribution:
then E(X)=....................
Probability distribution of X is given by
| X = x | 1 | 2 | 3 | 4 |
| P(X = x) | 0.1 | 0.3 | 0.4 | 0.2 |
Find P(X ≥ 2) and obtain cumulative distribution function of X
An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represents the number of black balls. What are the possible values of X? Is X a random variable?
A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.
Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
Let, X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that
where k is a positive constant. Find the value of k. Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.
Which of the following distributions of probabilities of a random variable X are the probability distributions?
(i)
| X : | 3 | 2 | 1 | 0 | −1 |
| P (X) : | 0.3 | 0.2 | 0.4 | 0.1 | 0.05 |
| X : | 0 | 1 | 2 |
| P (X) : | 0.6 | 0.4 | 0.2 |
(iii)
| X : | 0 | 1 | 2 | 3 | 4 |
| P (X) : | 0.1 | 0.5 | 0.2 | 0.1 | 0.1 |
(iv)
| X : | 0 | 1 | 2 | 3 |
| P (X) : | 0.3 | 0.2 | 0.4 | 0.1 |
The probability distribution function of a random variable X is given by
| xi : | 0 | 1 | 2 |
| pi : | 3c3 | 4c − 10c2 | 5c-1 |
where c > 0 Find: c
The probability distribution function of a random variable X is given by
| xi : | 0 | 1 | 2 |
| pi : | 3c3 | 4c − 10c2 | 5c-1 |
where c > 0 Find: P (1 < X ≤ 2)
Let X be a random variable which assumes values x1, x2, x3, x4 such that 2P (X = x1) = 3P(X = x2) = P (X = x3) = 5 P (X = x4). Find the probability distribution of X.
Two cards are drawn from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
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.
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
Find the mean and standard deviation of each of the following probability distribution :
| xi : | 1 | 2 | 3 | 4 |
| pi : | 0.4 | 0.3 | 0.2 | 0.1 |
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 |
A discrete random variable X has the probability distribution given below:
| X: | 0.5 | 1 | 1.5 | 2 |
| P(X): | k | k2 | 2k2 | k |
Determine the mean of the distribution.
Two cards are drawn simultaneously from a pack of 52 cards. Compute the mean and standard deviation of the number of kings.
A die is tossed twice. A 'success' is getting an odd number on a toss. Find the variance of the number of successes.
A box contains 13 bulbs, out of which 5 are defective. 3 bulbs are randomly drawn, one by one without replacement, from the box. Find the probability distribution of the number of defective bulbs.
Mark the correct alternative in the following question:
For the following probability distribution:
| X: | −4 | −3 | −2 | −1 | 0 |
| P(X): | 0.1 | 0.2 | 0.3 | 0.2 | 0.2 |
The value of E(X) is
Mark the correct alternative in the following question:
For the following probability distribution:
| X : | 1 | 2 | 3 | 4 |
| P(X) : |
\[\frac{1}{10}\]
|
\[\frac{1}{5}\]
|
\[\frac{3}{10}\]
|
\[\frac{2}{5}\]
|
The value of E(X2) is
Mark the correct alternative in the following question:
Let X be a discrete random variable. Then the variance of X is
For the following probability density function (p. d. f) of X, find P(X < 1) and P(|x| < 1)
`f(x) = x^2/18, -3 < x < 3`
= 0, otherwise
Calculate `"e"_0^circ ,"e"_1^circ , "e"_2^circ` from the following:
| Age x | 0 | 1 | 2 |
| lx | 1000 | 880 | 876 |
| Tx | - | - | 3323 |
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 )
A random variable X has the following probability distribution :
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| P(X) | C | 2C | 2C | 3C | C2 | 2C2 | 7C2+C |
Find the value of C and also calculate the mean of this distribution.
Determine whether each of the following is a probability distribution. Give reasons for your answer.
| x | 0 | 1 | 2 |
| P(x) | 0.4 | 0.4 | 0.2 |
Determine whether each of the following is a probability distribution. Give reasons for your answer.
| z | 3 | 2 | 1 | 0 | -1 |
| P(z) | 0.3 | 0.2 | 0.4. | 0.05 | 0.05 |
Find the probability distribution of the number of successes in two tosses of a die if success is defined as getting a number greater than 4.
There are 10% defective items in a large bulk of items. What is the probability that a sample of 4 items will include not more than one defective item?
The probability that a bulb produced by a factory will fuse after 200 days of use is 0.2. Let X denote the number of bulbs (out of 5) that fuse after 200 days of use. Find the probability of (i) X = 0, (ii) X ≤ 1, (iii) X > 1, (iv) X ≥ 1.
10 balls are marked with digits 0 to 9. If four balls are selected with replacement. What is the probability that none is marked 0?
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
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 :
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 :
Find the probability of the number of successes in two tosses of a die, where success is defined as six appears in at least one toss.
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
Consider the probability distribution of a random variable X:
| X | 0 | 1 | 2 | 3 | 4 |
| P(X) | 0.1 | 0.25 | 0.3 | 0.2 | 0.15 |
Calculate `"V"("X"/2)`
The probability distribution of a random variable X is given below:
| X | 0 | 1 | 2 | 3 |
| P(X) | k | `"k"/2` | `"k"/4` | `"k"/8` |
Determine P(X ≤ 2) and P(X > 2)
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 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: The value of A if E(X) = 2.94
Find the mean of number randomly selected from 1 to 15.
Two balls are drawn at random one by one with replacement from an urn containing equal number of red balls and green balls. Find the probability distribution of number of red balls. Also, find the mean of the random variable.
