. If the probability density function of a random variable X is given by { Determine (i) k (ii) the distribution function for X f (x) = 2k x e-*², for x>0 0, for x ≤0
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- 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) =Suppose that the unknown X is uniformly distributed between 0 and 2. What is the expected value of (4X3 + 1)?If the joint probability distribution of X and Y is given by * x+y f(x,y) = for x = 30 0,1,2,3; y = 0,1,2. Find the marginal distribution of Y X f(x, y) 1 2 3 1 2 3 30 30 2 30 4 1 Y 30 2 30 3 30 4 30 2 30 30 30 30 Y 1 2 y 1 2 f(y) 1 1 3 f(y) 1 7 10 10 5 3 15 If none of the choices, fill the table Y 1 2 | 0 |1 |2 | 3 f(y) 1 3 f(x) - 10 3 15
- (50) Let X be a random variable with p.d.f. k 17. If a random variable has the probability density function -1≤x≤3 otherwise f(x)=k(x²-1) =0let x be a discrete random variable with probability function p(x)= cx/20 for x = 2,3,4,5,6,8,12 what is the value of c that makes p(x) a valid probability function?2. The discrete random variable X has the probability function kx, P(X = x) = }k(x – 2), 0, x = 2,4,6 x = 8 otherwise Where k is a constant. (a) Show that k %3D 18 (b) Find the exact value of F(5).3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.Suppose X is a discrete random variable which only takes on positive integer values. For the cumulative distribution function associated to X the following values are known: F(23) 0.34 F(29) = =0.38 F(34) 0.42 F(39) 0.47 F(44) = 0.52 F(49) 0.55 F(56) = 0.61 = Determine Pr[29Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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