Q 2 If X is a random variable with distribution X: 0 1 2 3 4 P(X): 0 K 2K 3K 4K Explain the following: (i) For which value of K, P(X) is probability mass function? (ii) Find the following probabilities: (a) P(1 ≤X < 4). (b) P(2 < X < 4).

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: 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: 4 Evaluate -1 0 5 by: 3 - 2 expanding along the first row expanding along the second column A A 1.…

A:

Q: Find L{1}ℒ{1}.

A:

Q: 6/4 - 2/4

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

Q: 7 items chosen 5 at a time

A:

Q: 4 3/4 - 2 5/6

A: Given that the expression is

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: 20/5+5+2*8

A: Consider the given expression

Q: Randomly drawing and immediately three red M&Ms in a row from a bag that contains 10 red M&Ms out of…

A: Given: 30 total M&amp;Ms in that 10 red M&amp;Ms.

Q: factors of 20 that add up to 9

A:

Q: coefficient of variaton for given populaion   5,8,9,11,15,16,17,19

A:

Q: 1/5 + 1/10 + 1/15

A: Sum of numbers

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

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

Q: 6 3/20 - 6 3/8

A:

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

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: 6（c)(d)

A: We shall use the properties of homomorphism to solve this question

Q: 22 7/8 - 7=

A: Given,