Advertisements
Advertisements
Question
Prove that if E(X) = 0, then V(X) = E(X2)
Advertisements
Solution
V(X) = E(X2) – [E(X)]2
= E(X2) – 0 {Given that E(X) = 0}
Var(X) = E(X2)
Hence proved.
APPEARS IN
RELATED QUESTIONS
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(1/2 "e"^(x/2), "for" x > 0),(0, "otherwise"):}`
Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred
The probability density function of the random variable X is given by
`f(x) = {{:(16x"e"^(-4x), x > 0),(0, x ≤ 0):}`
find the mean and variance of X
Choose the correct alternative:
Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins ₹ 36, otherwise he loses ₹ k2, where k is the face that comes up k = {1, 2, 3, 4, 5}. The expected amount to win at this game in ₹ is
Choose the correct alternative:
Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E(X) and E(Y) respectively are
Find the expected value for the random variable of an unbiased die
Let X be a random variable defining number of students getting A grade. Find the expected value of X from the given table:
| X = x | 0 | 1 | 2 | 3 |
| P(X = x) | 0.2 | 0.1 | 0.4 | 0.3 |
How do you defi ne variance in terms of Mathematical expectation?
Choose the correct alternative:
If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to
Choose the correct alternative:
A discrete probability function p(x) is always non-negative and always lies between
