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Suppose that a random variable X 15 distributed according to the Gramma distribution with mean: 10...
#5 please 2. Find the probability distribution function for the random variable representing picking a random real number between -1 and 1. (This is a piecewise defined function.) 3. Compute the mean of the random variable with density function if x>0 ed f(r) = if r < 0. 0 4. Compute the mean of the random variable with density function 2e (1 - cos x) if x >0 if r<O. f (x) = 5 Compute the variance and standard deviation...
Suppose that X is a continuous random variable with probability distribution Suppose that X is a continuous random variable with probability distribution O<x<6 18 (a) Find the probability distribution of the random variable Y-10X 3. fr o) 2 Edit for Sy s (b) Find the expected value of Y
Suppose that a random variable is normally distributed with mean μ and variance σ2 and we draw a random sample of 5 observations from this distribution. What is the joint probability density function of the sample?
If we have a random variable T distributed according to exponential distribution with mean 0.8 hours. What is the probability that T will be greater than 48 minutes?
4. (8 Marks) Suppose X is a random variable best described by a uniformly distribution or probability that ranges from 2 to 11. a) Write down the probability density function f(1). (1.5 points) b) Compute the following: i) mean (1.5 points) ii) standard deviation (1.5 points) iii) P(X < 3.858) (1.5 points) iv) P(-O< X <H+ o) (2 points)
Suppose that X is a continuous random variable with density pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if 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 ∈ (0.1, 0.9). (d) Calculate the mean and the variance of X. 9.) Suppose that X is a continuous random variable with density C(1x) if E...
Assume the random variable X is normally distributed with mean equal to 50 and standard deviation of 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(35<x<58) Assume the random variable X is normally distributed with mean u = 50 and standard deviation o= 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(35<X<58) Click the icon to view a...
Let X be a uniformly distributed continuous random variable that lies between 1 and 10. i. Sketch the probability density function for X. ii. Find the formula for the cumulative distribution for X and use it to compute the probability that X is less than 6
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...
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...