Question

The following table lists the probability distribution of a discrete random variable x:

x = 0,1,2,3,4,5,6,7

P(x) = 0.04, 0.11, 0.18, 0.22, 0.12, 0.21, 0.09, 0.03

a. The probability that x is less then 5:

b. The probability that x is greater then 3:

c. The probability that x is less than or equal ti 5:

d. The probability that x is greater than or equal to 4:

e. The probability that x assumes a value from 2 to 5:

Show work please would like to follow the steps to see how the answer was found to understand the problem thank you

Answer 1

Solution :

Given that x as 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7

P(x) as 0.04, 0.11, 0.18, 0.22, 0.12, 0.21, 0.09, 0.03

a. => P(x < 5) = P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1) + P(x = 0)

= 0.12 + 0.22 + 0.18 + 0.11 + 0.04

= 0.67

b. => P(x > 3) = 1 - P(x <= 3)

= 1 - [ P(x = 3) + P(x = 2) + P(x = 1) + P(x = 0) ]

= 1 - [0.22 + 0.18 + 0.11 + 0.04]

= 0.45

c. => P(x <= 5) = P(x = 5) + P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1) + P(x = 0)

= 0.21 + 0.12 + 0.22 + 0.18 + 0.11 + 0.04

= 0.88

d. => P(x >= 4) = P(x = 4) + P(x = 5) + P(x = 6) + P(x = 7)

= 0.12 + 0.21 + 0.09 + 0.03

= 0.45

e. => P(2 <= x <= 5) = P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)

= 0.18 + 0.22 + 0.12 + 0.21

= 0.73