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- EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.EXER 6.3 Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 6 0 28 6 1 28 2 0 333333 28 28 28 2120 28 0None
- Let X1 , X2 , X3 be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The mean and variance of p-hat = 1/n ( X1 + X2 +... Xn ) . E(p-hat)= p Var(p-hat) = p(1-p) / nSuppose X is a random variable such that E(X) = 90 and Var(X) = 7. Compute thefollowing: E(4X + 12) Var(−X) SD(4X)E(X^2) E(X + 3)^2Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).
- Suppose that X₁, X₂, Xn and Y₁, Y2, . Yn are independent random samples from populations with means ₁ and ₂ and variances of and o2, respectively. Show that X - Y is a consistent estimator of μ₁ - 2.Suppose that the random variable X satisfies P(X=a) = p and P(X=b) = 1-p, where a<b. Verify that var(X) is largest for p=0.5Suppose that X is a geometric random variable with parameter π. Show that P(X = n+k|X > n) = P(X = k).
- 2.) For a continuous random variable X,where c is any one isolated number what is: P(X = c) Hint: For continuous random variables we always calculate things like: P(a10. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf f₂ (ylx) of Y.. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B bulb lasts at least 400 hours. d) Given that a Type B bulb fails at 300 hours, find the probability that a Type A bulb lasts longer than 300 hours. e) What is the expected total lifetime of two Type A bulbs and one Type B bulb?3 4 Let X be a random variable with f(x)=< 1 25x53. 4 0 otherwise a) Find and graph F(x). uct Find the value associated with the 90th percentile. b)SEE MORE QUESTIONS
