Suppose X is a uniform random variable with a = -15 and b = 45 . a. Fill in the

Question

Suppose X is a uniform random variable with a = -15 and b = 45 .

a. Fill in the blanks.

The mean of X is _______. (Give your answer as a whole number .)
The variance of X is _______. (Give your answer as a whole number .)
The standard deviation of X is _______. (Give your answer to four decimal places.)

b. Fill in the blank. (Round your answer to two decimal places.)

P(-10 <X <-1) is _______.

c. Fill in the blank. (Round your answers to four decimal places.)

P(X >0) is _______.

P(X 0) is _______.

d. Fill in the blank. (Give your answer to four decimal places .)

P( X20|X10) is _______.

Explanation / Answer

A) mean = (-15 + 45) / 2 = 15

Variance = (45 - (-15))2 /12 = 300

Standard deviation = sqrt(300)= 17.32

B) P(-10 < X < -1) = (-1 - (-10)) /(45 - (-15)) = 9/60= 0.15

C) P(X > 0) = (45 - 0) / (45 - (-15)) = 0.75

P(X > 0) = P(X > 0) = 0.75

D) P(X > 20 and X > 10) = P(X > 20) = (45 - 20)/(45 - (-15)) = 0.42

P(X > 10) = (45 - 10) / ( 45 - (-15)) = 0.58

P(X > 20 | X > 10) = P(X > 20 and X > 10)/P(X > 10) 0.42 / 0.58 = 0.72

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