Advertisements
Advertisements
प्रश्न
A random variable X has the following probability distribution:
then E(X)=....................
पर्याय
0.8
0.9
0.7
1.1
Advertisements
उत्तर
(a) 0.8
|
X = x |
-2 |
-1 |
0 |
1 |
2 |
3 |
|
P(x) |
0.1 |
0.1 |
0.2 |
0.2 |
0.3 |
0.1 |
`E(X)=sumx_iP(x_i)`
=( -2) x 0.1 + ( -1) x 0.1+ 0 x 0.2 +1x 0.2+ 2 x 0.3 + 3 x 0.1
= - 0.2 - 0.1 + 0 + 0.2 + 0.6 + 0.3
=0.8
APPEARS IN
संबंधित प्रश्न
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?
Find the probability distribution of number of tails in the simultaneous tosses of three coins.
Find the probability distribution of number of heads in four tosses of a coin.
The random variable X has probability distribution P(X) of the following form, where k is some number:
`P(X = x) {(k, if x = 0),(2k, if x = 1),(3k, if x = 2),(0, "otherwise"):}`
- Determine the value of 'k'.
- Find P(X < 2), P(X ≥ 2), P(X ≤ 2).
There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean 'and variance of X.
Two cards are drawn from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
Find the probability distribution of the number of heads, when three coins are tossed.
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.
An urn contains 4 red and 3 blue balls. Find the probability distribution of the number of blue balls in a random draw of 3 balls with replacement.
Find the mean and standard deviation of each of the following probability distributions:
| xi : | 2 | 3 | 4 |
| pi : | 0.2 | 0.5 | 0.3 |
Find the mean and standard deviation of each of the following probability distribution :
| xi : | -2 | -1 | 0 | 1 | 2 |
| pi : | 0.1 | 0.2 | 0.4 | 0.2 | 0.1 |
Two cards are drawn simultaneously from a pack of 52 cards. Compute the mean and standard deviation of the number of kings.
A fair coin is tossed four times. Let X denote the number of heads occurring. Find the probability distribution, mean and variance of X.
A fair die is tossed. Let X denote twice the number appearing. Find the probability distribution, mean and variance of X.
In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.
If a random variable X has the following probability distribution:
| X : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P (X) : | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |
then the value of a 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
Mark the correct alternative in the following question:
The probability distribution of a discrete random variable X is given below:
| X: | 2 | 3 | 4 | 5 |
| P(X): |
\[\frac{5}{k}\]
|
\[\frac{7}{k}\]
|
\[\frac{9}{k}\]
|
\[\frac{11}{k}\] |
The value of k is .
Calculate `"e"_0^circ ,"e"_1^circ , "e"_2^circ` from the following:
| Age x | 0 | 1 | 2 |
| lx | 1000 | 880 | 876 |
| Tx | - | - | 3323 |
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 |
The probability that a bomb dropped from an aeroplane will strike a target is `1/5`, If four bombs are dropped, find the probability that :
(a) exactly two will strike the target,
(b) at least one will strike the target.
A die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of at most 2 successes.
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 X = 0
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
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 non-negative
Solve the following problem :
The probability that a lamp in the classroom will burn is 0.3. 3 lamps are fitted in the classroom. The classroom is unusable if the number of lamps burning in it is less than 2. Find the probability that the classroom cannot be used on a random occasion.
Solve the following problem :
In a large school, 80% of the students like mathematics. A visitor asks each of 4 students, selected at random, whether they like mathematics.
Calculate the probabilities of obtaining an answer yes from all of the selected students.
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
Find the probability distribution of the maximum of the two scores obtained when a die is thrown twice. Determine also the mean of the distribution.
The probability distribution of a discrete random variable X is given below:
| X | 2 | 3 | 4 | 5 |
| P(X) | `5/"k"` | `7/"k"` | `9/"k"` | `11/"k"` |
The value of k is ______.
For the following probability distribution:
| X | – 4 | – 3 | – 2 | – 1 | 0 |
| P(X) | 0.1 | 0.2 | 0.3 | 0.2 | 0.2 |
E(X) is equal to ______.
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.
Two numbers are selected from first six even natural numbers at random without replacement. If X denotes the greater of two numbers selected, find the probability distribution of X.
A primary school teacher wants to teach the concept of 'larger number' to the students of Class II.
To teach this concept, he conducts an activity in his class. He asks the children to select two numbers from a set of numbers given as 2, 3, 4, 5 one after the other without replacement.
All the outcomes of this activity are tabulated in the form of ordered pairs given below:
| 2 | 3 | 4 | 5 | |
| 2 | (2, 2) | (2, 3) | (2, 4) | |
| 3 | (3, 2) | (3, 3) | (3, 5) | |
| 4 | (4, 2) | (4, 4) | (4, 5) | |
| 5 | (5, 3) | (5, 4) | (5, 5) |
- Complete the table given above.
- Find the total number of ordered pairs having one larger number.
- Let the random variable X denote the larger of two numbers in the ordered pair.
Now, complete the probability distribution table for X given below.
X 3 4 5 P(X = x) - Find the value of P(X < 5)
- Calculate the expected value of the probability distribution.
