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"):}`
If µ and σ2 are the mean and variance of the discrete random variable X and E(X + 3) = 10 and E(X + 3)2 = 116, find µ and σ2
Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred
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:
A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is
Find the expected value for the random variable of an unbiased die
In a business venture a man can make a profit of ₹ 2,000 with a probability of 0.4 or have a loss of ₹ 1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?
Choose the correct alternative:
Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are
Choose the correct alternative:
Which of the following is not possible in probability distribution?
Choose the correct alternative:
The distribution function F(x) is equal to
