Suppose X ∼ Binom(n, p). Show that E[X] = np.

Q: Ex. Show that [b, c) ~ [a, o), where a, b, c ER and b< c. [H7-9]

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Q: then -A U= 4 5 and uTu · [

A: The given matrix

Q: . Prove that an→L = Jan] → |L]. (Make cas

A: Given that an is a sequence which converges to L that is, an→L. Then we have to prove that |an|…

Q: There are 5 types to solve linear diff. eq. of first order * True False

A: Given that , Linear differential equation-A linear differential equation is defined by the linear…

Q: Let R = [1, 2] × [1, 2]. Compute ye*"dA. R

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Q: Suppose X~N(19, 2.5).  Find P(X = 17)

A: Given X~N(19, 2.5)

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: To show that the group &lt;a, b | a^5 = b^2 = e, ba = a^2b&gt; is isomorphic to Z2, we need to…

Q: Suppose X~ Unif (a, b). Show Vark) = (b-a) ² 12

A: Solution-: Given: X→U(a,b) We want to show Var(X)=(b-a)212

Q: Show that is isomorphic to Z2.

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Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

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Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

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Q: Show that (a + b)x = ax + bx for all a, b E F and all x € F¹.

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Q: If X, Y, Z ER and x≤Z, show that XL Y S z if and only if |x-y| + | y-z| = |x-z). Interpret…

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Q: 9. Let X Bin(4,.30), compute a. P(X=0) b. P(X= 1) C. P(X= 4)

A: Given that  Success of probability p=0.3 , q=1-p=0.7 Number of trials n=4 X~binomial (n,p)…

Q: how did the y' and 2y' apearred out of no where in line 7

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Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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