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. Additional Problem 6. Let X be a continuous random variable with...
Additional Problem 3. If X is a continuous random variable having cdf F, then its median...
Additional Problem 3. If X is a continuous random variable having cdf F, then its median is defined as that value of m for which F(m) = 0.5. Find the median for random variables with the following density functions (a) f(r)-e*, x > 0 (c) f(x) 6r(1-x), 1. Additional Problem 6. Let X be a continuous random variable with pdf (a) Compute E(X), the mean of X (b) Compute Var(X), the variance of X. (c) Find an expression for Fx(r),...
Let X be uniformly distributed in the unit interval [0, 1]. Consider the random variable Y...
Let X be uniformly distributed in the unit interval [0, 1]. Consider the random variable Y = g(X), where c^ 1/3, 2, if x > 1/3 g(x)- (a) Compute the PMF of Y b) Compute the mean of Y using its PMF (c) Compute the mean of Y by using the formula E g(X)]9)fx()d, where fx is the PDF of X
6. Let Y be a random variable with p.d.f. ce-4y for y20 (a) Determine c. (b)...
6. Let Y be a random variable with p.d.f. ce-4y for y20 (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y)/(E[Y)2? (c) Compute PríY < 5) (d) Compute PrY >5 |Y>1) (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that Pr(Y > q} 0.7?
3. (10 points) Let X be a continuous random variable with CDF for x < -1...
3. (10 points) Let X be a continuous random variable with CDF for x < -1 Fx(x) = { } (x3 +1) for -1<x<1 for x > 1 and let Y = X5 a. (4 points) Find the CDF of Y. b. (3 points) Find the PDF of Y. c. (3 points) Find E[Y]
6. Let Y be a random variable with p.d.f. ce4y for y 2 0 (a) Determine...
6. Let Y be a random variable with p.d.f. ce4y for y 2 0 (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y)/(E[Y])2? (c) Compute PríY <5) (d) Compute PríY >5 Y >1) (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that PriY >
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y...
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
Let X be a continuous random variable with the following density function. Find E(X) and var(X)....
Let X be a continuous random variable with the following density function. Find E(X) and var(X). 6e -7x for x>0 f(x) = { for xso 6 E(X) = 49 var(X) =
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y),...
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、
Let X be a continuous random variable uniformly distributed on the unit interval (0, 1), .e...
Let X be a continuous random variable uniformly distributed on the unit interval (0, 1), .e X has a density f(x) = { 1, 0<r<1 f (x)- 0, elsewhere μ+ơX, where-oo < μ < 00, σ > 0 (a) Find the density of Y (b) Find E(Y) and V(Y)
Additional Problem 4. We say that mp is the pth quantile of the distribution function F...
Additional Problem 4. We say that mp is the pth quantile of the distribution function F if F(mp) = p, 0<p<1. Find mp for the distribution having the following density functions: (a) f(x) = 5e*r, x > 0. (b) f(x) = ir', 0 < x < 2. -1<r1
Additional Problem 3. If X is a continuous random variable having cdf F, then its median is defined as that value of m for which F(m) = 0.5. Find the median for random variables with the following density functions (a) f(r)-e*, x > 0 (c) f(x) 6r(1-x), 1. Additional Problem 6. Let X be a continuous random variable with pdf (a) Compute E(X), the mean of X (b) Compute Var(X), the variance of X. (c) Find an expression for Fx(r),...
Let X be uniformly distributed in the unit interval [0, 1]. Consider the random variable Y = g(X), where c^ 1/3, 2, if x > 1/3 g(x)- (a) Compute the PMF of Y b) Compute the mean of Y using its PMF (c) Compute the mean of Y by using the formula E g(X)]9)fx()d, where fx is the PDF of X
6. Let Y be a random variable with p.d.f. ce-4y for y20 (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y)/(E[Y)2? (c) Compute PríY < 5) (d) Compute PrY >5 |Y>1) (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that Pr(Y > q} 0.7?
3. (10 points) Let X be a continuous random variable with CDF for x < -1 Fx(x) = { } (x3 +1) for -1<x<1 for x > 1 and let Y = X5 a. (4 points) Find the CDF of Y. b. (3 points) Find the PDF of Y. c. (3 points) Find E[Y]
6. Let Y be a random variable with p.d.f. ce4y for y 2 0 (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y)/(E[Y])2? (c) Compute PríY <5) (d) Compute PríY >5 Y >1) (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that PriY >
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
Let X be a continuous random variable with the following density function. Find E(X) and var(X). 6e -7x for x>0 f(x) = { for xso 6 E(X) = 49 var(X) =
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、
Let X be a continuous random variable uniformly distributed on the unit interval (0, 1), .e X has a density f(x) = { 1, 0<r<1 f (x)- 0, elsewhere μ+ơX, where-oo < μ < 00, σ > 0 (a) Find the density of Y (b) Find E(Y) and V(Y)
Additional Problem 4. We say that mp is the pth quantile of the distribution function F if F(mp) = p, 0<p<1. Find mp for the distribution having the following density functions: (a) f(x) = 5e*r, x > 0. (b) f(x) = ir', 0 < x < 2. -1<r1
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