Question

The probability distribution for the random variable x follows. x f(x) 20 0.20 25 0.15 30 0.30 35 0.35 (a) Is this probability distribution valid? Explain. Since f(x) 0 for all values of x and f(x) = , this a proper probability distribution. (b) What is the probability that x = 30?

Answer 1

Answer:

(a) The probability distribution is valid.

(b) The probability that x = 30 is 0.30.

Step-by-step explanation:

The probability distribution of the random variable X is:

   x:  20   |  25  |  30   |   35

f (x): 0.20 | 0.15 | 0.30 | 0.35

(a)

The properties of a probability distribution are:

1. 0 ≤ P (X) ≤ 1
2. ∑ P (X) = 1

All the probability value are more than 0 and less than 1.

Compute the sum of all the probabilities as follows:

$\sum P(X)=0.20+0.15+0.30+0.35=1$

The sum of all probabilities is 1.

Thus, the probability distribution is valid.

(b)

Consider the probability distribution table.

The probability of X = 30 is,

P (X = 30) = 0.30.

Thus, the probability that x = 30 is 0.30.