9. For n = 1,..,n, let X, be independent r.v.'s such that %3D P(X,=1)= p,, P(X,=0)=1- p,- Under what conditions on the p, 's, X, - 0, as n→ ∞.

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A:

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A: Find the anti derivative.

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A: Using the conditions of cubic spline,

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A: Topic : numerical methods

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A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

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A:

Q: 3. Recall that x - Poisson(0) = Mz(t) = e"(e*-1). %3D A. Derive the MGF of Z = (F - 0)/ /0/n where F…

A: Please find the solution below. Thank you.

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A: It is asked to find the marginal pdf's of X and Y. Marginal pdf of X. fx(x) = ∫0132y² dy=32∫01y²…

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A: Solution:

Q: Q11 Determine all the critical points for the following- S(x) = sin'x- cosx On the interval (0, 2n).

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Q: Let TNN(u,6²). define a faction Fact):= 2t- a, t>a, and Fact):= K (a-), tsa Find the value of a that…

A: Given:

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Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

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A: by limit convergence test we cab prove this, we have to treat the definite integral as summation…

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Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

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Q: 11 ComputePydz - zy'dy, nhere Dis descnbed by z² + y²s1. -1/2

A: Given an integral : ∫∂D x2y dx - xy2 dy  where D is : x2+y2≤1 We need to compute the integral.

Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

A:

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A: Suppose that u(x,t) is defined by a PDE and by initial values (at t=0)∂tu+t∂xu=u for all x,and…

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A: Given: SA = 1000 μx=0.04δ=0.02 Premium = 1.2P

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Q: ( If X₁, X2,..., Xn constitute a random sample of size n from a population given by 2(0 - x) for…

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Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

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A: please see the next step for solution

Q: in c nurmal disribution X= S and Z= -1.23 thờ tlis Yon that X-5 the mean Stardard devictens to The

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A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

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Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.