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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- 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]A random variable Z is normally distributed with mean and variance are 0 and 1 respectively. Determine the probability of P(√2 ≤ Z < √5)Consider the distribution of Binomial, Poisson, Exponential, Gamma, and let T1=X+4 and T2=(X-1) Check the property of biasdness
- A random variable Z is normally distributed with mean and variance are 0 and 1 respectively. Determine the probability of P( √2q12X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 3/4 of the expectation of X (ie Var(X)=0.75E(X)). The probability that X is less than 2 is equal to_____. Please fill in the blank.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