2. For the following discrete variable with probability f(x) X 1 2 4 f(x) 0.2 0.15 2c 0.05 0.15 By using CDF Determine P(1.1
Q: 2. For the following discrete variable with probability f(x) 1 3 4 f(x) 0.2 0.15 2c 0.05 0.15 (b)…
A: Given:
Q: *3. Let Z ~ N(0,1) and W x2 be independent. Find the distribution of: T =
A: Solution
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Q: 4 The random variable X has p.d.f. 1 f(x) = for -2 <x<4 = 0 otherwise. (i) Sketch the graph of f(x).…
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Q: 4) If X be a r.v. having t-distribution, then the value of e such that P(X>c)=0.05 is: a) 0.718. b)…
A: From the given information we find the t Value.
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Q: 1<x < 3 | f(x) = {C(x - 1)(3 – x) diğer
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Q: 5. If X and Y have the joint probability distribution f(x, y)=1/4, for x=-1and y=-1,x=-1 and y=1,x=1…
A: Given: fx,y=14=0.25 The joint probability function is shown below X -1 1 Y -1 0.25…
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A: Uniform distribution is widely used in statistics . It is very useful in modern times .
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Q: Suppose that X is normally distributed with u = 10 ando 2. Find P(IX 10|S3)
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Q: 2. For the following discrete variable with probability f(x) X 1 2 3 4 5 f(x) 0.2 0.15 2c 0.05 0.15…
A: Given:
Q: 3. If X has a uniform distribution in (0,1) with p.d.f f(x)=1, 0<x<1 = 0, otherwise. Find the…
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Q: 3. Let us consider two discrete uniform distributions X ~ U({1,2,..., k}) and Y U({0, k}). Compute…
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A: Given: The probability density function of random variable X is given as:…
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A: Given info: The probability P(X=x)=0, for a continuous variable
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A: Introduction :Here we have ,
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Q: 1. If X has the distribution function 0 for x1) e. P(-0.4 <X< 4) f. P(X = 5) 114
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A: The Probability Density Function is given as, Px=1225x This function is defined for x∈1,2,3,4.…
Q: 5. If X and Y have the joint probability distribution f(x, y)=1/4, for x=-1and y=-1,x=-1 and y=1,x=1…
A: Given: fx,y=14=0.25 The joint probability function is shown below X -1 1 Y -1 0.25…
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Q: The following is a probability distribution function for X, with range 0, 1, 2, 3: P(X = 0) = 0.2…
A: We have given that P(X = 0) = 0.2 P(X = 1) = 0.2 P(X = 2) = 0.3 P(X = 3) = 0.3 Hence we have…
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- If a random variable X has a discrete uniform distribution. fx(x)=1/k for x=1,2,..,k;0 otherwise. Derive P.G.F of X and compute E(2x+1)When a certain glaze is applied to a ceramic surface, the probability is 5% that there will be discoloration, 20% that there will be a crack, and 23% that there will be either discoloration or a crack, or both. Let X = 1 if there is discoloration, and let X = 0 otherwise. Let Y = 1 if there is a crack, and let Y = 0 otherwise. Let Z = 1 if there is either discoloration or a crack, or both, and let Z = 0 otherwise. a) Let pX denote the success probability for X. Find pX. b) Let pY denote the success probability for Y. Find pY. c) Let pZ denote the success probability for Z. Find pZ. d) Is it possible for both X and Y to equal 1? e) Does pZ = pX + pY? f) Does Z = X + Y? Explain.3.) Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)? What is P(X = 0)?
- Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?Suppose X and Y are jointly discrete randam variables, the conditional expectation of v(y),given that X= x,isLet X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0
- 5. Why the probability P(X=x)=0, for a continuous variable,?Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. n = 4, x = 1. n = 2, x = 2 n = 2, x = 0.1. Suppose that the amount X dispensed by a beverage-dispensing machine has a uniform probability distribution on [a, b] (in Ounces). (a) Given a and b, find x0 such that P(X < μ+x0) = 0.90, where μ = E[X]. (b)Given an i.i.d. sample X1, . . . , X200, explain how to estimate θ = b − a. Is the proposed estimator unbiased?
- If a probability generating function of a random variable x is Px(s)=(1/3+2/3s)^6 determine E(x),var(2x) and pr(X>1)Calculate the test-statistic, t with the following information.n1=45n1=45, ¯x1=2.55x¯1=2.55, s1=0.4s1=0.4n2=55n2=55, ¯x2=2.85x¯2=2.85, s2=0.38s2=0.38Rounded to 2 decimal places.Let (Ω, Pr) be a probability space, and let X and Y be two independent random variables that are positive and have non-zero variance. (a) Prove that X2 and Y are independent. Note that by symmetry, it will also follow that Y 2 and X are independent. (b) Use the result from part (a) to show that the random variables W = X + Y and Z = XY are positively correlated (i.e. Cov(W, Z) > 0).