Question

In: Statistics and Probability

For each probability and percentile problem, draw the picture. Let X ~ Exp(0.15). a. Sketch a...

For each probability and percentile problem, draw the picture.

Let X ~ Exp(0.15).

a. Sketch a new graph, shade the area corresponding to P(X < 7), and find the probability. (Round your answer to four decimal places.)

b.Sketch a new graph, shade the area corresponding to P(2 < X < 7), and find the probability. (Round your answer to four decimal places.)

c. Sketch a new graph, shade the area corresponding to P(X > 7), and find the probability. (Round your answer to four decimal places.)

d. Sketch a new graph, shade the area corresponding to the 40th percentile, and find the value. (Round your answer to two decimal places.)

e. Find the average value of X. (Round your answer to two decimal places.)

Solutions

Expert Solution

The CDF of the distribution is

a)  The area corresponding to P(X < 7) is shaded below.

The probability is

b) The area corresponding to  P(2 < X < 7)is shaded below.

The probability is

c)  The area corresponding to P(X > 7) is shaded below.

The probability is

d) The 40-the percentile is

The region is shaded below.

e) The average value of the exponential distribution is

orchestra answered 1 year ago
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