1. Determine L{t*}. n! Ans. s*+1

Q: Q2/ Fin x in the

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Q: Consider an experiment Consting of independent rolls of a fair die, let W record the number f times…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Suppose that the number of subsets with k elements, made out of a set of n elements is called by the…

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Q: dz 4. Compute where

A: We can solve the problem by residue method

Q: Show for all natural numbers n >= 3 that [(1 + (1/n))^n] < n.

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Q: 10. If w is FALSE, x is TRUE, and y is FALSE, what is ((w OR Y') AND (x' AND y')') OR ((w OR y') AND…

A: Given :If w is FALSE, x is TRUE, and y is FALSE.To find : ((w OR y') AND (x' AND y')') OR ((w OR…

Q: ppose that 100 tags, numbered 1,2,..., 100, are placed into an urn, and s are drawn successively,…

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Q: If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1)…

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Q: consider J = & @= <-4,8. Find 1lat-4w|l

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Q: 1)r =4rsin e

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Q: Which of the following statements is FALSE? Select one: If events A, B and Care independent, then A…

A: Option  b and  Option c is false. Because from the option b is given that the symbol is less than…

Q: Let Ch= k! (k-n)!n! denote the binomial coefficient. For fixed n, show that and thus ACK = Cik n…

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Q: Suppose that A= {a,b,c,d} Then |A| =.?

A: Let X be a set , then X be number of elements in set X

Q: To show B(m,n)=+x²² -dx (1+x)"¹"

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Q: Prove that 3! 2(n+3) = = n r=0 (-1) 1 n "Cr r+3 Cr

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Q: Suppose that an ordinary deck of 52 playing cards will be randomly ordered, and then the cards will…

A: Given information: Given that the ordinary deck consists of 52 playing cards. The cards will be…

Q: In a resort in Mexico guests may have dinner at three restaurants, the Italian restaurant, the…

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Q: A cinema can accomodate 200 customers. Let z denotes the numbers of the customers in cinema. What…

A: Introduction: It is given that the cinema can accommodate 200 customers. The random variable z…

Q: 15. Use a 30-60-90 triangle to find the tangent of 60°. 2 /60° 1 30% √3

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Q: Give a combinatorial proof for the identity 1+2+3+..+n= (",").

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Q: 1) A, = 0, 1, 1, 2, 2;, 3, 3;, 4..; find the 40h term and the sum of the first "21 terms.

A: Nothing

Q: 61 8. (*+1)

A: Please refer the attached image for complete solution.

Q: Four club vans carrying 150 cricket players from the club and arrive at a cricket ground. The van…

A: The total number of vans are four and total number of players are 150. The probability of a variable…

Q: (b) Prove that E-o(-1)* )= 0 for all positive integers m.

A: We have to prove ∑k=0n-1kkn=0 for all positive integer n

Q: 6xy÷(20cyrax-3y)

A: To evaluate: -6xy ÷(2xy+x×-3y) Let's simplify first inside bracket , therefore -6xy ÷(2xy-3xy) ⇒-6xy…

Q: X={1,2,3,4} find permutations S4=

A: Consider  X= {1,2,3,4}

Q: 9) If X-N(68,7.29), then p(X < 65) =

A: normal distribution  x~N(68,7.29)

Q: Suppose U ~ Binomial(n, p) and n > 2. What is P(U > 1)?

A: Solution

Q: Show that sup{ 1- n: n EN} = 1.

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Q: If n> 5 is an integer, prove the identity () - OO(;)-O0C:")- O0(:)--(":)OO +..+ by counting in two…

A: We are given a formal containing sum of binomial coefficients and we have to prove it using two…