Advertisements
Advertisements
Question
The random variable X can take only the values 0, 1, 2, 3. Give that P(X = 0) = P(X = 1) = p and P(X = 2) = P(X = 3) such that `Sigmap_i x_i^2 = 2Sigmap_ix_i`. Find the value of p
Solution
It is given that the random variable X can take only the values 0, 1, 2, 3.
Given:
P(X = 0) = P(X = 1) = p
P(X = 2) = P(X = 3)
Let P(X = 2) = P(X = 3) = q
Now,
P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 1
`=> p + p + (q + q) = 1`
`=> q = (1- 2p)/2`
Since, `Sigmap_ix_i^2 = 2Sigmap_ix_i`
`=> 0 + p(1)^2 + ((1-2p)/2)(2^2 + 3^2) = 2[0 + p + ((1-2p)/2) (2 + 3)]`
`=> p + 13/2 (1- 2p) = 2[p + 5/2(1-2p)]`
`=> p + 13/2 - 13p = 2p + 5 - 10p`
`=> 13/2 - 12p = -8p + 5`
`=> 4p = 3/2`
`=> p = 3/8`
RELATED QUESTIONS
A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.
In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).
The random variable X can take only the values 0, 1, 2, 3. Given that P(2) = P(3) = p and P(0) = 2P(1). if `Sigmap_ix_i^2 = 2Sigmap_ix_i`, Find the value of p.
Find the mean and variance of the number of tails in three tosses of a coin.
Find the mean, variance and standard deviation of the number of tails in three tosses of a coin.
Find the expected value, variance and standard deviation of the random variable whose p.m.f.’s are given below :
| x = x | 1 | 2 | 3 |
| P (X = x) | `1/5` | `2/5` | `2/5` |
Find the expected value, variance and standard deviation of the random variable whose p.m.f.’s are given below :
| x = x | -1 | 0 | 3 |
| P (X = x) | `1/5` | `2/5` | `2/5` |
Find the expected value, variance and standard deviation of the random variable whose p.m.f.’s are given below :
| x = x | 1 | 2 | 3 | ... | n |
| P (X = x) | `1/n` | `1/n` | `1/n` | ... | `1/n` |
Find the expected value, variance, and standard deviation of the random variable whose p.m.f.’s are given below :
| x = x | 0 | 1 | 2 | 3 | 4 | 5 |
| P (X = x) | `1/32` | `5/32` | `10/32` | `10/32` | `5/32` | `1/32` |
Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings drawn.
Let X be a discrete random variable assuming values x1, x2, ..., xn with probabilities p1, p2, ..., pn, respectively. Then variance of X is given by ______.
Find the variance of the distribution:
| X | 0 | 1 | 2 | 3 | 4 | 5 |
| P(X) | `1/6` | `5/18` | `2/9` | `1/6` | `1/9` | `1/18` |
A die is tossed twice. A ‘success’ is getting an even number on a toss. Find the variance of the number of successes.
The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:-
Suppose that two cards are drawn at random x from a deck of cards. Let x be the number of aces obtained. Then value of E(x) is
Three friends go for coffee. They decide who will pay the bill, by each tossing a coin and then letting the “odd person” pay. There is no odd person if all three tosses produce the same result. If there is no odd person in the first round, they make a second round of tosses and they continue to do so until there is an odd person. What is the probability that exactly three rounds of tosses are made?
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distnbution of the number of spade cards.
