Question

1. Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.)

x	P(x)
4	0.10
7	0.25
10	0.30
13	0.35

2. Given a binomial distribution with n = 6 and π⁢= .25. Determine the probabilities of the following events using the binomial formula. (Round your answers to 4 decimal places.)

1. x = 2

2. x = 3

3. A probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. The outcomes are mutually exclusive, and the list of outcomes is exhaustive.

True or False

Answer 1

1)

Mean = X * P(X)

= 4 * 0.10 + 7 * 0.25 + 10 * 0.30 + 13 * 0.35

= 9.7

Variance = X² * P(X) - Mean²

= ( 4² * 0.10 + 7² * 0.25 + 10² * 0.30 + 13² * 0.35 ) - 9.7²

= 8.91

2)

For binomial distribution,

P(X) = ⁿC_x^X ( 1 - )^n-X

P( X = 2) = ⁶C₂ 0.25² 0.75⁴

= 0.2966

P( X = 3) =  ⁶C₃ 0.25³ 0.75³

= 0.1318

3)

The characteristics of probability distribution is

i) The probability of outcome is between 0 and 1 inclusive.

ii) The outcomes are mutually exclusive.

iii) The list of outcomes are exhaustive. That is sum of probabilities equal to 1.

Therefore, given statement is TRUE.