Question

In: Statistics and Probability

1. Let X1, X2 be i.i.d with this distribution: f(x) = 3e cx, x ≥ 0...

1. Let X1, X2 be i.i.d with this distribution: f(x) = 3e cx, x ≥ 0 a. Find the value of c

b. Recognize this as a famous distribution that we’ve learned in class. Using your knowledge of this distribution, find the t such that P(X1 > t) = 0.98.

c. Let M = max(X1, X2). Find P(M < 10)

Expert Solution

a.

For valid PDF,

For c < 0,

c = -3

b.

The distribution function is,

which is an exponential distribution with rate parameter = 3

P(X1 > t) = 0.98.

3t = ln(0.98)

t = 0.00673

c.

CDF of M is,

X1, X2 are i.i.d .

(Using CDF of exponential distribution)

= 1 * 1

= 1

orchestra answered 2 years ago

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