Let X be a continuous random variable with the following cumulative distribution function: x<0 2 F(x) = 2x 1 2 Then P(0.4
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- 3) Suppose X is a discrete variable that has the following pr function (pdf) f (X) 1. 0.40 0.20 3 0.15 4. 0.25 a) Calculate the cumulative distribution function (the b) Find the expected value, showing your work: E(X) c) Find the variance, showing your work: Var (X)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(18)=0.4F(25)=0.44F(33)=0.5F(41)=0.53F(46)=0.56F(52)=kF(57)=0.64F(65)=0.67 Assuming that Pr[25<X≤52]=0.17, determine the value of k.Consider the following discrete probability distribution:- X 2 4 6 8 10 P(X = x) 0.3 0.3 0.2 0.1 0.1 Find: P(X < 8) E[X] Variance (X) If Y = 2X + 5, find E[Y]
- c) Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {₁ - e-²x Determine the expected value of X. } " x ≥ 0Let X be a random variable representing number of times the system needs to be repaired before the claim of full failure. The probability mass function of X is given in the following distribution table: X1 2 3 1 3 1 f(x) 10 5 10 Then Variance of X is equal to: 0.84 1.01 1 O None of theseSuppose 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 youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON