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3 years ago

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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 d

istribution 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?

1 answer:

Damm [24]3 years ago

6 0

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 <em>X</em> is:

<em> x</em>: 20 | 25 | 30 | 35

f (<em>x</em>): 0.20 | 0.15 | 0.30 | 0.35

(a)

The properties of a probability distribution are:

0 ≤ P (X) ≤ 1
∑ 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 <em>X</em> = 30 is,

P (X = 30) = 0.30.

Thus, the probability that x = 30 is 0.30.

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