Let x represent a binomial random variable with parameters n and p. Show that (a) E(x) : = n(n − 1)p²; (c) E[x(x - 1)(x − 2)] mp; (b) E[x(x − 1)] - = - - 1)(n − 2)p³; -

A fair coin is tossed three times and the random variable x equals the total number of heads. Find the sketch F(x) and f(x).

A baseball team claims that the mean length of its games is 2.4 hours. State H0 and Ha in words and in symbols. Then determine whether the hypothesis test for this claim is​ left-tailed, right-tailed, or​ two-tailed. Explain your reasoning.       State the null hypothesis in words and in symbols. Choose the correct answer below.     A. The null hypothesis expressed in words​ is, "the mean length of a baseball​ team's games is at most 2.4 ​hours." The null hypothesis is expressed symbolically​ as, ​"H0​: μ≤2.4​."   B. The null hypothesis expressed in words​ is, "the mean length of a baseball​ team's games is more than 2.4 ​hours." The null hypothesis is expressed symbolically​ as, ​"H0​: μ≠2.4​."   C. The null hypothesis expressed in words​ is, "the mean length of a baseball​ team's games is at least 2.4 ​hours." The null hypothesis is expressed symbolically​ as, ​"H0​: μ≥2.4​."   D. The null hypothesis expressed in words​ is, "the mean length of a baseball​…

A3 Let X₁,..., Xn be independent and identically distributed random variables with E(X₂) μ and Var(X₂) = o². Let X = 1 X₁/n. Which of the following statements are true? (i) E(X) = μ/(n-1) (ii) E(X) = μ (iii) X is an unbiased estimator for μ (iv) E(X) = μ/n A: (i), (ii), and (iii) Circle the correct letter: B: (i) and (iii) C: (ii), (iii), and (iv) D: (ii) and (iii) E: (ii) and (iv) A B = CDE