 # Random Variables

To Access the full content, Please Purchase

• Q1

Define mean of a random variable.

Marks:1

Suppose a random variable X assumes the values x1, x2, ..., xn with probabilities of occurrence p1, p2, ..., pn respectively. Then the mean of the random variable X is defined as

E(x) = x1p1 + x2p2+... xnpn = ∑xp.

• Q2

Two bad eggs are mixed accidentally with 10 good one. Find the probability distribution of one bad egg in three, drawn at random, from this lot.

Marks:1 • Q3

Check whether the following can be probability distribution of a random variable X:

 X: 0 1 2 P(X): 0.3 0.5 0.1

Marks:1

P(X = 0) + P(X = 1) + P(X = 2) = 0.3 + 0.5 + 0.1
= 0.9 ≠ 1

Hence, the given distribution of probabilities is not a probability distribution.

• Q4

Define random variable.

Marks:1

A random variable is a real valued function having domain as the sample space associated with a random experiment.

• Q5

If X is a random variable and k is a constant then prove that

Var(kX) = k2VarX.

Marks:1

Var(X) = E(X2) – [E(X)]2

Var(kX) = E(k2X2) – [E(kX)]2

= k2E(X2) – [kE(X)]2

= k2E(X2) – k2[E(X)]2

= k2[E(X2) – {E(X)2}]

= k2Var(X)