7. Find the variance of X, given X ∼ Bin(n = 15, p = 0.13)
a. 1.3025
b. 13.05
c. 1.6965
d. 1.95
Assume that X~ Bin(n, p) Find the variance of X algebraically. Hint: First find E(X(X-1)) Use M () to find V(X) 1. а. b.
1. Let X ~ Bin(n = 12, p = 0.4) and Y Bin(n = 12, p = 0.6), and suppose that X and Y are independent. Answer the following True/False questions. (a) E[X] + E[Y] = 12. (b) Var(X) = Var(Y). (c) P(X<3) + P(Y < 8) = 1. (d) P(X < 6) + P(Y < 6) = 1. (e) Cov(X,Y) = 0.
3. Let X~ Bin(n,p) with n known (a) State the parameter space for the mode b) State EX] and V[x]. (c) Is p an unbiased estimator for the population proportion p? Show why or why not (d) To estimate the variance of X, we generally use θ 2Pl1 ow is a estimator for V지. (e) Modify 0 from part (b) to form an unbiased estimator for V[X ].
2. Suppose X - Unif (0, 1) and S, |X ~ Bin(n, X). Let I, indicate the ith trial is a success. This 10, find: implies that llx ~iid Bern(p a) P(S1o 3) X). For n c) P(I11 1S10 3) d) P(l111, 12 1S10 3) 2. Suppose X - Unif (0, 1) and S, |X ~ Bin(n, X). Let I, indicate the ith trial is a success. This 10, find: implies that llx ~iid Bern(p a) P(S1o 3) X). For...
Let X ∼ Bin(n = 20, p = 0.25) be a Binomial r.v. with parameters n = 20, p = 0.25. Given that X does not exceed 5, what is the probability that X takes an even value?
2. Let X~Bin(n, p) with n known. State whether the following expressions are statistics or not. If an expression is not a statistic, explain why. (a) The number of successes X observed in n trials The sample proportion of successes D (c) z -, where X ~ N(5,4) p-P (d)-p I-D
For n=5 and p=0.13, what is P(X=0)?
Y~Bin(n,p). 15 of 100 samples are successes. Test the null hypothesis H0 : p = 0.10 against the alternative Ha : p > 0.10 at level alpha = 0.1 Find the p value.
if x~bin 7,1/4 find p(x=6)
15)Find the value of x, given DE¯¯¯¯¯¯¯¯∥BC¯¯¯¯¯¯¯¯, AD=x+33, BD=x+13, AE=18, and CE=10. Question 15 Find the value of , given DE || BC, AD = 7+33, BD = 1 + 13, AE = 18, and CE = 10. B D P с E a) O 12 b) 09 c) O 10 d) O 15 N e) None of the above