Let X1, X2,...,X, be a random sample from a N(u, o²) population. Define X = , Xị. (a) If u is unknown and o? is known, show that Z = n(X- Ho)/o is a Wald statistic for testing Ho : H = Ho- (b) If u is unknown and o? is known, show that Z = vn(X - Ho)/o is also a Score statistic for testing Ho : 4 = Ho. (c) The moment generating function (MGF) of X ~ N(H, o²) is Mx(t) = exp(ut+). Use the MGF to show that X follows a N(u, o?/n) distribution. %3D %3D 2

Q: How many even 3-digit numbers can be formed from the digits 1, 3, 4, 8, and 9 with no repetitions…

A: Out of the total 5 digits 1, 3, 4, 8 and 9 given, the even digits are 4 and 8. For the 3- digit…

Q: factors of 24 that add up to 10

A: factors of 24 that add up to 10

Q: 21 2. 6.

A:

Q: 2/18 – 12/32 + 3V50

A: The solution is given below in the next step:

Q: 4 2 G F -8 -4 -2 2 10 -2 -4 E 10 K 00

A: Formula for area is length multiply by breadth. Similarly for square its a^2 if side of square is…

Q: How many ordered triples of letters are there taken from the letters A, T, C, and G?

A: given letters: A,T,C and Gtotal number of letters = 4

Q: A = 6 -2 -2 10 -3 5 1 ---3-0 C=0-2 a = 1, b = [3 08]. -10 1 . B 5 2 11 9 4 4 7 0 0 11

A: We have to solve given Questions.

Q: Find L{1}ℒ{1}.

A:

Q: 2/5+4/8

A: We have to find the sum

Q: 4. Determine (16-912) dt c4

A: We will solve the problem.

Q: -7 5 1 9 0 -2 -1 2 -1 4

A:

Q: 6/4 - 2/4

A: Explanation and solutions is given below.....

Q: 4n – 1

A:

Q: 6 2/5 + 1 3/10

A:

Q: (5V3)2

A: Explanation of the solution is given below...

Q: n?_4

A:

Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: find  3/4 + 1/8

A:

Q: 9/12+3/24

A:

Q: 1/4 +5/4

A: Solution: The objective is to find the value of the given expression

Q: 5 7/12 + 1 3/4 + 4 1/2

A: Given that 5712+134+412Solution  :5712+134+412=57+39+24612

Q: 9 5/12 - 3 2/3 =

A: Case 1: Let the given number be in mixed fraction notation.

Q: expansion of (1-2m)“

A:

Q: Evaluabe: 25+3 se

A: Here we find Laplace inverse transform

Q: 5. Find the coefficient of a¹¹b4 in the expansion of (a + b)¹5.

A:

Q: 29 Using the combination formula expand (5+x)

A:

Q: Compute the indicated product.   -1 3   9 2 0   3 9 3

A:

Q: 5 2/5+ n= 75/6

A: Given query is to find the value of n.

Q: 土4 7

A:

Q: 4) /

A: Using By Parts rule of integration.

Q: 1. Use expansion along the 3rd row -4 3 1 2 -1 1 7 5

A:

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.