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- 4. The cumulative distribution function of a continuous random variable, X is given as follows: x<0 F(x) = - x(x+4), 32 0Sx<4 1 x24 (a) Calculate P(|X-1|<1). (b) Find the median. (c) Determine the probability density function of X. Hence, evaluate E(3X² -1).Let X be a random variable with probability density function [ a + bx², 01. Let X have the probability density function f(x) = cx(1-2) for 0≤x≤ 1 and f(x) = 0 otherwise. (a) Show that c = 6. (b) Find the cumulative distribution function F(x) = P(X ≤ z). (c) Calculate P(.1 < X <5). (d) Find the mean, variance and standard deviation of X.b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following probability density function: f(x;0)=√√2n0 0, -20₁ if -∞0 < x <∞0 otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 0.a) Let X be a continuous random variable with the following probability density function (2x3 f(x)={11 2 +5) , 0Lori Jeffrey is a successful sales representative for a major publisher of college textbooks. Historically, Lori obtains a book adoption on 36% of her sales calls. Viewing her sales calls for one month as a sample of all possible sales calls, assume that a statistical analysis of the data yields a standard error of the proportion of 0.08. (a) How large was the sample used in this analysis? That is, how many sales calls did Lori make during the month? (c) Using the sampling distribution of p, compute the probability that Lori will obtain book adoptions on 46% or more of her sales calls during a one-month period. (Round your answer to four decimal places.)b) Let X₁, X2, X3.....Xn be a random sample of n from population X distributed with the following probability density function: ze zo, f(x;0)=√2m0 0, (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. if -∞If 2 > 0 and X is a continuous random variable with p. d.f. 22xe-dx ,x 2 0 ,otherwise f(x) = Then var(X) is:If F(x) is cumulative distrbution function of a continuous random variable X, the probability (function f(x) is the dervative of F(x (Fa)se (TrụeRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON