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2. Let X be a continuous random variable with pdf ( cx?, [xl < 1, f(x)...
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1,...
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf ( cx?, |a| 51, f(x) =...
2. Let X be a continuous random variable with pdf ( cx?, |a| 51, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise...
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
2. Let X be a continuous random variable with pdf ca2, 1 f(x) otherwise, where the...
2. Let X be a continuous random variable with pdf ca2, 1 f(x) otherwise, where the parameter c is constant (with respect to x) (a) Find the constant c (b) Compute the cumulative distribution function F(x) of X (c) Use F(x) (from b) to determine P(X 1/2) (d) Find E(X) and V(X)
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)
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
5. Let ffx)= cx for 1 < x< c0, zero otherwise be the pdf for the...
5. Let ffx)= cx for 1 < x< c0, zero otherwise be the pdf for the random variable X. a) Find c b) Find F(x). c) Find P(X> 3.2). d) Find E(X).
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called...
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
b. Let X be a continuous random variable with probability density function f(x) = kx2 if...
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F()...
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf ( cx?, |a| 51, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
2. Let X be a continuous random variable with pdf ca2, 1 f(x) otherwise, where the parameter c is constant (with respect to x) (a) Find the constant c (b) Compute the cumulative distribution function F(x) of X (c) Use F(x) (from b) to determine P(X 1/2) (d) Find E(X) and V(X)
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)
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
5. Let ffx)= cx for 1 < x< c0, zero otherwise be the pdf for the random variable X. a) Find c b) Find F(x). c) Find P(X> 3.2). d) Find E(X).
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
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