Advertisements
Advertisements
Question
Prove that V(X + b) = V(X)
Advertisements
Solution
L.H.S = V(x + b)
= E(x + b)2 – [E(x + b)]2
= E(x2 + 2bx + b2) – [E(x) + b]2
= E(x2) + 2bE(x) + b2 – [E(x)]2 + b2 + 2bE(x)]
= E(x2) + 2bE(x) + b2 – [E(x)]2 + b2 – 2bE(x)]
= E(x2) – [E(x)]2
= V(x)
= R.H.S
L.H.S = R.H.S
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) = {{:(1/10, x = 2"," 5),(1/5, x = 0"," 1"," 3"," 4):}`
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(2(x - 1), 1 < x ≤ 2),(0, "otherwise"):}`
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"):}`
A lottery with 600 tickets gives one prize of ₹ 200, four prizes of ₹ 100, and six prizes of ₹ 50. If the ticket costs is ₹ 2, find the expected winning amount of a ticket
Find the expected value for the random variable of an unbiased die
In investment, a man can make a profit of ₹ 5,000 with a probability of 0.62 or a loss of ₹ 8,000 with a probability of 0.38. Find the expected gain
What do you understand by Mathematical expectation?
Define Mathematical expectation in terms of discrete random variable
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:
A discrete probability distribution may be represented by
