2. Show that for all n ≥ k ≥ 0, n (1)-(²) = k k

Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: 9. Establish the Bernoulli inequality: If 1 + a > for all n ≥ 1. (1+a)" 0, then 1+ na

A:

Q: Show that for all x>0, e* >1+x+÷ 2.

A:

Q: Show that it is not true that for every error 1/m there exists n such that |Ek=1 polt – r/(1 - r)| <…

A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

Q: S 6(1 – y), 0<x <y<1 (.) - {0, elseubere x, Y elsewhere

A:

Q: Find a closed formula for S(n, n − 2), for all n ≥ 2.

A: Find a closed formula for S(n, n − 2), for all n ≥ 2.

Q: 63. Given n nonzero numbers o1,...,on, show that the minimum value of S(x1....,xn) = xfo7 +..+ x…

A:

Q: 8. Find a number o such that if 0 < x − 2| < 8,then | 3x − 1| < &,where s=0.06.

A:

Q: 15. Let z = 2cos0 + i(1 – 2sin0) where -n < 0 < n Show that Iz – il = 2

A:

Q: (b) For any n ≥ 1, the factorial function, denoted by n!, is the product of all the positive…

A:

Q: Let X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently. 1.…

A: X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently.

Q: 2. (a) Show that k!n-k-1 = for n>0 and ka nonnegative integer. 5. e-nxxk dx

A:

Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

A: From the given information, W follows normal distribution with mean µ=-1 and variance σ2=4.

Q: that for n > k we Sn+1 ||

A: The expression given is ,  n+1k+1=∑j=knnn-jjk The number of ways to partition n+1 objects into k+1…

Q: Prove that for n ≥ 1: 1k² = n(n + 1)(2n + 1).

A: Given that  to prove for n≥1, ∑k=1nk2=16n(n+1)(2n+1)

Q: 1) Consider the conquer and divide relation f(n) = 2f (n / 4) +9 with f(1) = 3. a. Considering only…

A: Here we try to find the pattern so that we can find the general formula.