Suppose that X is a random variable from a binomial distribution with parameters n=12 and p. Consider the point estimate p̂=X/14
1. what's the bias of this estimate?
2. what is the value of the mean square error of this estimate if
the actual value of p is 0.735
Suppose that X is a random variable from a binomial distribution with parameters n=12 and p....
need process thx Part 1 of 4 - Written Answer #1 Suppose that X is a random variable from a binomial distribution with parameters n = 12 and p and consider the point estimate: p=8/14 (Enter your final answers only in the space provided and submit your work to obtain the answers on Gradescope.) Question 1 of 2 0.0 Points What is the bias of this point estimate? What is the value of the mean square error of this point...
Suppose that a random variable X follows a binomial distribution. Find the bias of each of the following estimators. Be sure to follow your computations enough to determine whether the estimator is biased or unbiased. a. p̂ = (X+1)/(n+2) b. p̂ = X2/n2 c. p̂ = X/n
Problem 6: Suppose we observe a random variable X having a binomial distribution with parameters n and zp. (a) What is the generalized likelihood ratio for testing Ho : p-0.5 against H, : p* 0.5? (b) Show that a generalized likelihood ratio test rejects Ho when |X -n/2|2 c. (Hint: it may help to consider the logarithm of the generalized likelihood ratio.) (c) What is the significance level of the test when n 12 and c 5? Problem 6: Suppose...
3. Suppose Xi, X2, and X are independent random variables drawn from a binomial distribution with parameters p and n. The observed values are Xi -3, X2-4, and (a) Suppose n 12 and p is unknown. What is the maximum likelihood estimator (b) Suppose p - 0.4 and n is unknown. What is the maximum likelihood estimator for p? for n? (Note: Since n is discrete you can't use calculus for this; just write the formula and use trial and...
Let X be a random variable, which has a binomial distribution with parameters n and p. It is known that E(X) = 12 and Var(X) = 4. Find n and p.
Problem 5. Let X be a binomial random variable with parameters n and p. Suppose that we want to generate a random variable Y whose probability mass function is the same as the conditional mass function of X given X-k, for some k-n. Let a = P(X-k), and suppose that the value of a has been computed (a) Give the inverse transform method for generating Y. (b) Give a second method for generating Y (c) For what values of a,...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...
Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the following probabilities using the binomial formula. a.) P( x = 5) b.) P( x = 8) c.) P( x = 12) d.) P( x ≤ 4) e.) P( x ≥ 8) f.) P( x ≤12)
A random variable X has binomial distribution with parameters n = 11 and theta = 0.28. P(X > 2) = ________________
Suppose X is a binomial distribution with parameters n and p. Find the Bias and MSE of the following estimators for p (а) Өт (b) Ө2 (c) For which values of p is MSE(e1) < MSE(e2)? х X+1 n+2