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Q1) (20 Mark) The probability density function of a random variable X is given by: f(x)...
Q1) (20 Mark) The probability density function of a random variable X is given by: f(x)...
Q1) (20 Mark) The probability density function of a random variable X is given by: f(x) Cx-2 x21 1) Find the value of C 2) Find the distribution function F(X) 3) Find P(X > 3) 4) Find the mean and the standard deviation of the distribution
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451...
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise....
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f()...
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) =...
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) = { a, 35x55 2 - bx, 5 < x < 6 elsewere 10 i)Find the value of a and b and hence, sketch f(x) ii) Find the cumulative distribution function, f(x) and sketch it.
Q 2. The probability density function of the continuous random variable X is given by Shell,...
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
The probability density function of a random variable X is given by f(x) = { kae?...
The probability density function of a random variable X is given by f(x) = { kae? for > 0 for <0. 0 Find a) the value of k and b) the distribution function of X. (Hint: The integral lobe-du looks much simpler.)
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0...
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
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)
PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks...
PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks b) The life expectancy (in days) of a mechanical system has a probability density write down equations for the cumulative distribution C(x) and the survival distribution Px). State a relationship between them. function f(x)=1/x, for x21, and f(x)=0 for x <1. i Find the probability that the system lasts between 0 and I day.2 marks i) Find the probability that the system lasts between...
Q1) (20 Mark) The probability density function of a random variable X is given by: f(x) Cx-2 x21 1) Find the value of C 2) Find the distribution function F(X) 3) Find P(X > 3) 4) Find the mean and the standard deviation of the distribution
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) = { a, 35x55 2 - bx, 5 < x < 6 elsewere 10 i)Find the value of a and b and hence, sketch f(x) ii) Find the cumulative distribution function, f(x) and sketch it.
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
The probability density function of a random variable X is given by f(x) = { kae? for > 0 for <0. 0 Find a) the value of k and b) the distribution function of X. (Hint: The integral lobe-du looks much simpler.)
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
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)
PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks b) The life expectancy (in days) of a mechanical system has a probability density write down equations for the cumulative distribution C(x) and the survival distribution Px). State a relationship between them. function f(x)=1/x, for x21, and f(x)=0 for x <1. i Find the probability that the system lasts between 0 and I day.2 marks i) Find the probability that the system lasts between...
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