Suppose X is a continuous random variable such that P(X lessthanorequalto x) = {

Question

Suppose X is a continuous random variable such that P(X lessthanorequalto x) = {1 - e^-x^2/8 if x greaterthanorequalto 0 0 otherwise a. Find P(X lessthanorequalto 4). b. Find P(X > 2). c. Find P (1 lessthanorequalto X lessthanorequalto 3). d. Find P(X lessthanorequalto 2|X lessthanorequalto 4). A figure skating routine is designed to last six minutes. The amount of time (in minut less than or greater than six minutes is a random variable, with a probability density function given by f(x) = {Squareroot 2/pi - x^2 if - Squareroot 2/pi lessthanorequalto x lessthanorequalto Squareroot 2/pi

Explanation / Answer

6.24)

a)P(X<4)=1-e-4^2/8 =1-e-2 =0.8647

b)P(X>2)=e-2^2/8 =e-0.5=0.6065

c)P(1<X<3)=e-1^2/8-e-9/8 =0.8825-0.3247=0.5578

d)P(X<2|X<4)=P(X<2 & X<4)/P(X<4) =P(X<2)/P(X<4) =(1-0.6065)/0.8647=0.4551

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