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Chapter 3: Q1E (page 116)

Suppose that a random variable X has the Bernoulli distribution with the parameter p = 0.7. (See Definition 3.1.5.) Sketch the c. d. f. of X.

Short Answer

Expert verified

P(X 鈮�1) = 0.3

Step by step solution

01

Given the information

A random variable X has the Bernoulli distribution with parameter p=0.7

02

Statement and find the c. d. f of X

A random variable Z that takes only two values, 0 and 1, with P(Z=1) = p, has the Bernoulli distribution with parameter p. Z is sometimes referred to as a Bernoulli randomized variable with value p.

The formula for c. d. f. of X

03

Calculations

Then we have given that it has a Bernoulli distribution with parameter p=0.7 means P(X=1) = 0.7, the equation that says

P(X 鈮�1) = 0.3

So, the c. d. f. would be 0 before x=0, then to 0.3, and then at x=1, it would be up to1

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