Question

Consider the following discrete probability distribution. x 15 22 34 40 P(X = x) 0.14 0.40 0.26 0.20 a. Is this a valid probability distribution? Yes, because the probabilities add up to 1. No, because the gaps between x values vary. b. What is the probability that the random variable X is less than 40?

Answer 1

Answer:

(a) Yes, because the probabilities add up to 1.

(b) The probability that X < 40 is 0.80.

Step-by-step explanation:

The probability distribution of the random variable X is:

   x:  15   |   22  |   34   |   40

f (x): 0.14 | 0.40 | 0.26 | 0.20

(a)

The properties of a probability distribution are:

1. 0 ≤ f (x) ≤ 1
2. ∑ f (x) = 1

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

Compute the sum of all the probabilities as follows:

$\sum f(X)=0.14+0.40+0.26+0.20=1$

The sum of all probabilities is 1.

Thus, the probability distribution is valid.

(b)

Consider the probability distribution table.

Compute the probability of X < 30 as follows:

P (X < 40) = P (X = 15) + P (X = 22) + P (X = 34)

                $=0.14+0.40+0.26\\=0.80$

Thus, the probability that X < 40 is 0.80.