Let X be the random variable with the cumulative probability distribution: 0 F(x)= 1 = {xx ²₁ x < 0 02 Determine the value of k.
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- a) Consider the following probability density distribution of random variable X. if 0Assume that x donotes the continuous random varlable with probability distribution of y & (x) and cumulative distribution as ISU FCx) =3x - 2x x>1 What is the P(0.9< X S 2)?Let X represent a continuous random variable with a Uniform distribution over the interval from 0 to 2. Find the following probabilities (use 2 decimal places for all answers):(a) P(X ≤ 0.22) = (b) P(X < 0.22) = (c) P(0.98 ≤ X ≤ 1.92) = (d) P(X < 0.98 or X > 1.92) =Let X represent a continuous random variable with a uniform distribution over the interval from 0 to 4. What is P(X < 0.9)?A continuous random variable X has probability distribution function f(x) , wheref(x) = k(1 − x2) for − 1 < ? < 1. Calculate the P(X < 0)?A product is classified according to the number of defects, it contains (X1) and the factory that produces it (X2),. The joint probability distribution is given by X/X2 2 0 1/8 1/16 I/16 1/16 3/16 1/8 3 1/8 1/4 (a) Find the marginal distribution of X1A random variable X follows a uniform continuous distribution on the range [0, B]. Use mathematical expectation to show the mean is B/2Let X denote a random variable having a distribution. If F(x)=ax³ where 0≤x≤(+3). Find f(x) after getting the constant value (a) and find the probability P(2Find the characteristic function of X² when X has the N(u, o²) distribution.Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. n=56 p=0.5 x=30 A)For n=56, p=0.5, and X=30, use the binomial probability formula to find P(X). B)Can the normal distribution be used to approximate this probability? A. No, because np(1−p)≤10 B. Yes, because np(1−p)≥10 C. Yes, because np(1−p)≥10 D. No, because np(1−p)≤10 C) Approximate P(X) using the normal distribution. Use a standard normal distribution table. A. P(X)=enter your response here (Round to four decimal places as needed.) B. The normal distribution cannot be used. D) By how much do the exact and approximated probabilities differ? A.enter your response here (Round to four decimal places as needed.) B. The normal distribution cannot be used. E)By…Consider the random variable X with PDF (known as Cauchy distri- bution) f(x) = 7 - 00The probability distribution function of a random variable X is 4. P(X =x)=Dk for x=0,1, 2,3,4 where k is a constant. Determine (a) the value of k. Hence, find P(0SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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