Advertisements
Advertisements
प्रश्न
What are the properties of Mathematical expectation?
Advertisements
उत्तर
Properties of Mathematical expectation:
i. E(a) = a, where ‘a’ is a constant.
ii. E(aX) = aE(X)
iii. E(aX + b) = aE(X) + b, where ‘a’ and ‘b’ are constants.
iv. If X ≥ 0, then E(X) ≥ 0
v. V(a) = 0
vi. If X is random variable, then V(aX + b) = a2V(X)
APPEARS IN
संबंधित प्रश्न
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"):}`
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:
If P(X = 0) = 1 – P(X = 1). If E[X] = 3 Var(X), then P(X = 0) is
Let X be a continuous random variable with probability density function
`"f"_x(x) = {{:(2x",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
Find the expected value of X
Choose the correct alternative:
Probability which explains x is equal to or less than a particular value is classified as
Choose the correct alternative:
A discrete probability distribution may be represented by
Choose the correct alternative:
E[X – E(X)]2 is
Choose the correct alternative:
A listing of all the outcomes of an experiment and the probability associated with each outcome is called
Choose the correct alternative:
The distribution function F(x) is equal to
Prove that if E(X) = 0, then V(X) = E(X2)
