Question

In: Statistics and Probability

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a...

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere.

a) Find a so that f(x) is a probability density function

b)What is P(X<=1)

Expert Solution

(a)
The value of a is found by noting that the Total Probability = 1

So,

we get:

i.e.,

between the limits 0 to .

Applying limits, we get:

i.e.,

So

a = 3

Answer is:

3

(b)

So, the Probability Density Function of X is written as follows:

So,

between the limits 0 to 1

Applying limits, we get:

= 0.7982

So,

Answer is:

0.7982

orchestra answered 2 years ago

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