(20 pts) Determine the expectation, variance, standard deviation, cumulative distribution function (c.d.f.), and median for each...
5. (20 pts) Determine the expectation, variance, standard deviation, cumulative distribution function (c.d.f.), and median for each of the following: (a) f(x)-름 (z-1.5) for 2 rS 5 (b) f(x) = Lp (c) f(x) = d for 40 < x < 100 (d) f(x)- e-z/2 for x 20 1.25 for 1<x<5
(25 pts) Determine the expectation, variance, standard deviation, and cumulative distribution function (c.d.f.) for each of the following: 0 f(x)0.44 0.360.150.04 0.01 (b) f(x) = f for x = 1, 2, 3, 4 (c) f(x)-345 for1,2,4,5 d) A random variable that represents the outcome of rolling one (fair) die. (e) A random variable that represents the outcome of rolling two (fair) dice.
Determine the expectation, variance, standard deviation, and cumulative distribution function (c.d.f.) for each of the following: (a) x 0 1 2 3 4 f(x) 0.44 0.36 0.15 0.04 0.01 (b) f(x) = x 10 for x = 1, 2, 3, 4 (c) f(x) = 2 5x2−30x+45 for x = 1, 2, 4, 5 (d) A random variable that represents the outcome of rolling one (fair) die. (e) A random variable that represents the outcome of rolling two (fair) dice.
PART E ONLY 2. (25 pts) Determine the expectation, variance, standard deviation, and cumulative distribution function (c.d.f.) for each of the following: f(x)0.44 0.36 0.15 0.04 0.01 (b) f(x) = 끊 for z = 1, 2, 3, 4 (c) f(x) = 5F-302145 (d) A random variable that represents the outcome of rolling one (fair) die. (e) A random variable that represents the outcome of rolling two (fair) dice for 1,2,4,5
Measurement of a blood test is a random variable X with cumulative distribution function given by 0, 1, r >2 a. Find fx(x), the probability density function b. Graph fx(x) c. Find the mean and the variance of X d. Find the median of X
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.
Q1. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function F and density f. Let b>0. (a) Write the forinula for E(X b)+1. (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
Q2. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Let b> 0. (a) Find the cumulative distribution function of Y = XI(X < b} (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
Show steps, thanks! 2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.