Suppose Sn is the sum of 48 independent experimental values of the random variable X whose probability density function is fx(x) = { //, 1 ≤ x ≤ 4
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![Suppose Sn is the sum of 48 independent experimental values of the random variable X whose probability density function
is
fx(x)
1 ≤ x ≤ 4
otherwise
What is the probability that Sn is in the range [108, 126]? HINT: E[X] =
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- Suppose that X is a random variable having the following probability density function given by (2(0-x) x>0 f(x) = elsewhere Find the value of c such that an interval from x to cx is a (1-a)100% confidence interval for the parameter 8.The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.7. If a random variable has the probability density function -1≤x≤3 otherwise f(x)=k(x²-1) =0
- For the continuous probability function f(x) = Kx² ex when x ≥ 0 find i) k ii) mean iii) variance =(A=X) qand variance of X if the probability mass function is f(x) = ; ;)" , Find the moment generating function, mean x = 1, 2, 3, 4, ...Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?
- Let X be a Poisson random variable with rate X. Find the mgf of X.Find the expected value of the continuous random variable g(x)= x^2+3x+2, if the density function for random variable x are shown in the following equation. f() = [F(2x-1) 0Let X be a continuous random variable with range [−ln5,0] and its probability density function is given by the following function: f(x)=ce^−x, where cc is a constant. (1) Find the value of c . Answer: (2) Find the probability P(−ln2≤X≤0) . Answer:Let Zw distributed as Chi square random variable with n degree of freedom. Find the limiting distribution of Wn = Zw/n2Let X will be continuous random variable with probability density function as below. f(x) = {4x , (01.) Consider the discrete random variable with pmf: P(X=x)=(A/(4^x)), x=2,3,4,5,.... What is the value of A?Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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