Question

Consider the following probability distribution table:

X

1

2

3

4

P(X)

.1

.2

.3

.4

If Y = 2+3X, E(Y) is:

A.7 B.8 C.11 D.2

19.

If Y=2+3X, Var (Y) is:

A.9

B.14

C.4

D.6

20.

Which of the following about the binomial distribution is not a true statement?

A. The probability of success is constant from trial to trial. B. Each outcome is independent of the other. C. Each outcome is classified as either success or failure. D. The random variable of interest is continuous.

Answer 1

Solution :

Mean = = X * P(X)

= 1 * 0.1 + 2 * 0.2 + 3 * 0.3 + 4 * 0.4

= 0.1 + 0.4 + 0.9 + 1.6

E(X) = = 3

If Y = 2 + 3 X,

E(Y) = 2 + 3 E(X) = 2 + 3 * 3 = 2 + 9 = 11

E(Y) = 11

Option C)

variance

= X ² * P(X) - ²

=   1² * 0.1 + 2² * 0.2 + 3² * 0.3 + 4² * 0.4 - 3²

= 0.1 + 0.8 + 2.7 + 6.4 - 9

Var(X) = 1

If Y = 2 + 3 X,

Var (Y) = 9 Var(X) = 9 * 1 = 9

Var (Y) = 9

Option A)

Not a true statement about the binomial distribution is ,

D. The random variable of interest is continuous.