Given the probability density function f(x) = }x over [1, 3], find each of the following. 15. E(x) 16. E(x²) 17. The mean 18. The variance 19. The standard deviation
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- Consider the continuous random variable X = the weight in pounds of a randomly selected newborn baby born in the United States last year. Suppose that X can be modeled with a normal distribution with mean μ = 7.57 and standard deviation σ= 1.26. If the standard deviation were σ = 1.06 instead, how would that change the graph of the pdf of X?Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?Find E(X^2) when random variable X has normal distribution with mean(µ) = 7 and standard deviation(σ) = 4.
- Suppose that the probability density function of the length of computer cables is f (x) = 2x/(52) for x between 0 and 5 meters. Determine the standard deviation of the cable length. Please enter the answer to 2 decimal places.Suppose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square distribution with 2 degrees of freedom.Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?
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