Suppose that Y is an exponential random variable with λ = 4. Find. P[Y > (E(Y) + 2√√Var(Y))].

Q: If A=A(t) find the A? m d²A RT da -3Tcr 2 dt dt

A: We have to solve the homogeneous solution first.

Q: A random variable has a PDF f(x) = i) The value of C. ii) P (X> 2). √√25-x² -5<x<5. Find

A:

Q: You and your friends are invited to a party. The time of your arrival, X, is exponentially…

A: We are given that the time of arrival X is exponentially distributed with mean 2. This implies that…

Q: For numbers 10 to 12, given the following table showing the 1000 parts tested in a manufacturing…

A:

Q: Suppose John tosses a coin 5 times. Let X be the number of heads. Calculate Pr(X = x) for x = 0, 1,…

A: if a coin is tossed once than the p=P(getting a head)=12=0.5Let X=no.of headsX~Binomial(n=5 ,…

Q: [(√x-3) dx

A:

Q: Show that Q(V3, V3) = Q(v3+ V3) %3D

A:

Q: If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X…

A: Assuming X is the sample mean of the random samples,consider the following lemma:

Q: Evaluode Lim [x]+[2x ]+ n2

A: We know that, x-1&lt;x≤x Therefore, 2x-1&lt;2x≤2x ⇒3x-1&lt;3x≤3x . . . ⇒nx-1&lt;nx≤nx ∴ (x + 2x + 3x…

Q: If Z = eax + by F(ax - by); the value of %3D az is + a ду az

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Q: P(C|m')

A:

Q: Given P(D/M)=(P(M/D)P(D))/(PM), Solve the following 1. Discuss the True negative from the main…

A: Given: True negative from the main reverse tree

Q: (5)Find x if. i. e* = 3, ii. Inx = 2 iv. 32-x = 27, v. 8x+1 32. %3D

A:

Q: P(x) = 1. Let x! and let H=10, Find P(9)

A: To find: P(9)

Q: Suppose X-Geometric(p=3/4) and Y- Poisson(3) .  Find P(X&lt;=2). Find P(Y&lt;4 | Y&gt;=3) .  Assume…

A: Approach to solving the question:      Key references:

Q: Let flx)=x² and! gix)-Xr4. Find (gof)は) (fog)l-5)= (gof)(-5)= こくい(6。)

A: We have to find fog(x) ,gof(x)

Q: Let X be the number of times a fair die is rolled until one appears twice in a row. Find E(X).

A:

Q: 1. D, [3x²y+In(xy²)] За + In(xg In(xy³)]

A: Given,

Q: E (x. - x Y Show that is a consistent estimator for o is N (µ, o²).

A: ANSWER: For the given data,

Q: 5. y°(2x² + y?) = c². RESP. y? = 2x² In Įkx|.

A: We will find out the required general solution.

Q: The values for P(A₁B) and P(A₂B) were found to be 0.20 and 0.02, respectively. Use these values to…

A: The values for P(A1nB) and P(A2nB) were found to be 0.20 and 0.02 P(A1nB) = 0.20 P(A2nB) = 0.02 Find…

Q: P(5 SxS 17) =

A: Given, Mean = 8 standard deviation = 6

Q: 1-2x (c) Determine the values of a, b and c if =1+ax+ bx? + cx. Hence, by 1+2x, 1 show that 2 s 3,…

A:

Q: =e constant K when x > 0.) c so that c. /X₁ X₂)

A: Given as,  Xi follow exponential with mean λ.

Q: Let P(A) = 0.4 "and " P(AU B) = 0.6. For what value of P(B) are A "and " B are independent?

A:

Q: Let X1,., X idN(µ, o²). 3(x2 + + Xn-1), Xn X1 If u = ... 5(п - 3) 5 | find E(@) 3 (a) 5 (п-3) 3…

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Q: A fair coin is tossed three times and the random variable x equals the total number of heads. Find…

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Q: (a) Е(X), (Ь) var (X), (c) P(-2 <x < 0.5),

A: Let ,  The pdf of X is given by , = 0 ; otherwise Our aim is to find the following : a) E(X) b)…

Q: If P(A) = 0.2, P (B) = 0.4 and P (A |B)) = 0.1 Compute P(AUB) Enter your answer with two decimal…

A: Given,P(A) = 0.2P(B) = 0.4P(A|B) = 0.1

Q: Find​ p(x) for x=​0,​1, 2,​ 3, 4, 5.

A: Answer:- Given, The formula for probability distribution of X is,

Q: Let Xinexp(A). Sholw that T- Xi Sulficieay Statistics is

A: We will use the factorization theorem to determine the sufficient statistic.

Q: P(A | B) = .3, P(B) = .6, P(A | B') = .1. Find P(B | A).

A: Using the conditional probability P(A|B) and its formula we get: