Which range do i have to integrate?

Question

A continuous random variable X that can assume values between x = 2 and x=5 has a function density f(x) = 2(1+x)/27

Find P(X<4)

Answer 1

Step 1:

The function over the interval .

The function is continuous and non negative over the interval .

If is a continuous random variable with probability density function , the probability that assumes value in the interval between and is .

The function .

.

Step 2:

The function over the interval .

Find , the integral range between and .

.

Solution:

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