1. Compute the value of (), for n > 3.

Q: Given X~ N(20,16), find c. P( 19 < X<23) (4 decimal place)

A: X~N(20,16) Mean(μ)=20 Variance(σ2)=16 standard deviation(σ)=16=4

Q: (b) Compute the values of each of the following expressions: i. () ii. (1), (1) iii. (2), ), iv. 6).…

A: The expressions are given in the form .It represents the combination of  out of .The formula for…

Q: 10. Give a combinatorial proof: For n ≥ 1 and k ≥ 1, (n)k = n · (n − 1)k-1.

A: To give: A combinatorial proof: For n≥1 and k≥1, k·nk=n·n-1k-1.

Q: Determine the least upper bou You must fully justify your an

A: We have to find least upper bound of the given set

Q: Let X~N(10,9).

A: The mean of the distribution is 10. The standard deviation of the distribution is 9.

Q: 8. The (2*+1 – 2k) = %3D k=0

A:

Q: For all n ≥ 1, let an = (a) Find a1, a2, A3, A4. (b) Computea. i=1 (c) Computea. i=1 (n + 1)² n!…

A:

Q: 5. Prove that, for n> 1, n

A:

Q: 5.3.2 (a) Suppose that n > 3. Prove that ("+1)ʻ 5.

A: Given:-             n+1n2 &lt; 2 n+1n2 -22&lt;0n+1n+2n+1n-2&lt;0n+1n+2 =…

Q: 2.24 Derive the simplest sum-of-products expression for the function f(x₁, x2, x3, x4) X₁ X3 X4 +…

A: we have to derive the simplest sum-of-products expression for the functionFor the given function,…

Q: 81. Prove: 2+4 +6+ + 2n = n(n + 1). ...

A:

Q: 1. +1 Select one: a. th n! b. tn-1 (n 1)! C. n! tn+1 d. n! th-1 e. t+1 (n +1)!

A: Solution:-    L-11sn+1  ∵we know  that:-By using Laplace properties:-

Q: Show that (n) ‡ 14 for all n ≥ 1.

A:

Q: 4. Let h(r) = 5 x 6 20 x²3x18 Find all values of N for which h(N) = 3.

A:

Q: Alireza will take IE 4301 next semester and attend EVERY class in person. He will wear a mask to the…

A: Solution

Q: Q2: Let A = { all integers 1 more than a multiple of 3}, Let B = {all the integers 1 more than a…

A: According to the concepts of set theory, the word "or" is equivalent to the union of sets. According…

Q: C. Prove the following using PMI. 1. 1+4+7+... + (3n-2) = " (3H=1 for all n21. n (n+1) 2. 1+2+3+...…

A: We will prove the given statement using PMI.

Q: Calculate P(z<-1.2)

A: The z-score is standard normal variable with mean 0 and standard deviation 1.

Q: VI. Write the following in the Roster Method. 1. E><s} 2. {x\x is an odd integer between 0 and 10}…

A: According to our policy at Bartleby, I can solve only one question. We need to write the given set…

Q: 7. f : N2 → N.

A: (1) N2 ={(m,n): m,n∈N}     This is the sketch of the bijection f:N2 →N The curve which is traced on…

Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

A: The given function is                               sβ=q-2+q1+4q-1qβ122q-1 where β&gt;0 and q&gt;3.…

Q: 1. Suppose that for a certain life , S×(x) =1- 100 Find (i) Find the prob. that a person aged 25…

A: Given problem is :

Q: b) Evaluate UTM L{t*e- 6(t-2)}. TM

A:

Q: Which of the following statement is always false? (a) For all integer x, [x] = [-x] (b) For all odd…

A:

Q: 10. Suppose X-N (3.2) Find P (22}, P(X>3)

A: Given that v  X ~ N ( 3, 22 )  i.e. μ = 3 ? = 2 By using standard normal distribution we solve this…

Q: 3. Prove that 6|(9" - 3") for all n E Z+.

A:

Q: 1. Determine the value of x in the following (SHOW ALL WORK!!!). a) x = 5000(1.075)4(7) b) x = 100…

A:

Q: If n increases without end, 1/n becomes closer and closer to （ ） Does this make sense? If so, please…

A: For some negative n, when it is increased n value reaches to 0, for which the value of 1n reaches to…

Q: 5. Algebraically show that n-1 k- = n · k k-1

A:

Q: a) Let p=13. Compute L2(3) b) Show that L2(11) = 7.

A: Here concept of field is used.

Q: 5. For n ≥ 1, establish the formula (2n + 1)² = (4tn + 1)² – (4tn)².

A:

Q: Show that, for n > 1 2n 1.3.5... (2n – 1),2n 2.4.6...2n n

A:

Q: (iii) Differentiate the integral to get that fr(t) 2|t| = 1/2 500 £2² (1u). 2/11 u. fv (u)du, k k…

A: Given, U~χ2k, a chi-squared distribution with k degrees of freedom. fUu=1Ƶuk2-1e-u2, u&gt;0 T=ZUk,…

Q: Show that for n ≥ 3, ô(n) is even.

A: We have from the definition of Euler ϕ function: ϕ(1)=1 and ϕ(2)=1 Now Let n ≥ 3

Q: P(- c ≤ Z ≤ c)=0.9399

A: We have given that  P(- c ≤ Z ≤ c)=0.9399 From the given information we have to find the value of c

Q: 14. Let f(n) = n² + 20 and g(n) = n³. Show that f(n) is O(g(n)) by finding a positive integer N for…

A:

Q: 1. Let k and n be non-negative integers. (a) What does the function pr(n) count? (b) Show that the…

A: k and n are :Two non-negative integers.

Q: n Show that (") = (,“,) n-r.

A: