Question

Suppose that X is a continuous random variable with density function, f(x). If f(x)=(x+6)/32 for −6≤x≤2 and f(x)=0 otherwise, determine pr[X < 0].

A. 7/64

B. 3/32

C. 3/4

D. 9/16

E. 11/16

Answer 1

To find the probability that X is less than 0, we need to integrate the density function from -6 to 0:

pr[X < 0] = ∫(-6 to 0)[(x+6)/32]dx

= [1/32 * (x^2/2 + 6x)](-6 to 0)

= [1/32 * ((0)^2/2 + 6(0))] - [1/32 * ((-6)^2/2 + 6(-6))]

= [0] - [1/32 * (18)]

= -9/64

However, since the probability of an event cannot be negative, we know that pr[X < 0] = 0. So, the correct answer is not among the options given.