1 Let x be a continuous random variable with probability den

1) Let x be a continuous random variable with probability density function f(x) and cumulative distribution function f(x). Then for any two numbers a and b where a < b, which of the following is true?

A) P(X > a) = 1 - F(a)

B) P(a<= X <= b) = F(a) - F(b)

C) F(x)= (x-a)/(b-a)

D) P(X > b) = F(b) - 1

2) how many ways can a subset of size 4 be constructed from the set (a, b, c, d, e) when order within the subset matters?

A) 100

B) 120

C) 5

D) 24

Solution

1. F(a) = P(X <= a)

So, P(X>a) = 1 - P(X<=a) = 1 - F(a)

Answer: A) P(X > a) = 1 - F(a)

2. This is a case of permutations where 5 distinct things need to be arranged into 4 places where order matters

= 5P4 = 5C4*4! = 5*24 = 120

Answer: B) 120