Q3. The moment generating function for a random variable X is e3t M(t)=1-t2¹ What are the mean and the variance of X, respectively? -1 < t < 1.

Q: The variance, 6², of a probability distribution is used to describe the spread of the values of the…

A: GivenMean(μ)=E(x)=8 x x-μ (x-μ)2 f(x) (x-μ)2f(x) 4     0.25   8     0.50   12     0.25…

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3   We know…

Q: (1) Find the value of k which make the following function a pdf fly) = { (15/64) +(y/64) -1<= y <= 0…

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Q: A random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y.…

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Q: (b) The CDF F(x) of a random variable X is given by; if x 3 (i)find PDF f(x) (ii) P(|X| < 1.5),…

A: The P.D.F is given by: fx=ddxFx=ddxcx-14=4cx-13

Q: Let X and Y be independent random variables with means ux, μy and variances o, oy. Find an…

A: Given:  Random variable x and y are independent with means ux, uy  , varience σ2(x) and σ2(y)  E(x)=…

Q: Probabilities of values of X-[10 21 24 27 30], a random discrete variable, are [0.16 0.09 0.13…

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Q: EX7.8) Let Y be a random variable having a uniform normal distribution such that Y~U (2,5) Find the…

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Q: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

A: We want to findvalue of t

Q: Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by Fx(x) = {1 -…

A: Let X be a random variable with a cumulative distribution function (cdf) given byTo findThe…

Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

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Q: Let X have a mean of 132 and a variance of 32. Define Y=X² + 2X+1. Compute the (a) mean and (b)…

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Q: The random variable Y has the Poisson distribution with a mean of 50. (a) What is the variance of Y?…

A: Let Y have a Poisson distribution with a mean of 50.The PMF of Poisson distribution with a mean of…

Q: b. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.

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Q: Suppose that f (x) = x / 8 for 3 < x < 5. Determine the mean and variance of x.

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Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

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Q: Skewness is defined as ((X-μ)³/a) where is the mean and ² is the variance. If the exponential…

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Q: Let X be a geometric distribution function with px(n) = p(1 - p)n-¹. Find the expected value and the…

A: P(X=x)=p(1−p)x−1;x=1,2,3,...

Q: Find the MGF of the binomial distribution ()ra- Use it to show that the mean is p and the variance…

A: Given that the pmf of the binomial distribution is P(X=x)=nxpx1-pn-x, x=0, 1, 2,..., n. We have to…

Q: A random variable X has P(5<X<19) 2 0.75. Using Chebyshev's theorem, the mean and variance (H, o2)…

A: The mean will be the average of 5 and 19. So, mean= (5+19)/2=12

Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

A: given dates  p ( cancer) = 0.03 n = 10 patients  q = 1=p = 1-0.003 = 0.997

Q: Three random variables X₁, X₂, X3 have equal variances o2 and coefficient of correlation between X₁…

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Q: f X is a random variable such that: E(X) = 6.2 and E(X2) = 62.5, then what is the standard deviation…

A: Given: X is a random variable. E(X)=6.2 E(X2)=62.5

Q: W= X+ 3Y Find the (c) correlations (d) correlation coefficient of V and W

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Q: rva

A: To find the variance of the damage from a random hurricane.

Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

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Q: Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the…

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Q: The estimated variance function will be O Bo + B₁X + o² OV(Y|X) = ² O V(Y|X) = ² O None of the other…

A: It is given as the simple linear regression model Y = β0 + β1X + e, e ~iid N( 0, σ2 ), i = 1, 2, . .…

Q: f(x) = (2x + 1)/c, 0 ≤ x ≤ 4. Find the variance of the distribution. 438/c² 409.2/c² O 431.6/c² O…

A: The objective of the question is to find the variance of the distribution of the function f(x) = (2x…

Q: Consider a random sample from the distribution of Binomial, Poisson, Exponential, Gamma, and normal.…

A: Let Xi~Bn,p, the the p.m.f of Xi is given by, px=Cnxpxqn-x,x=0,1,2,...,n Then, EXi=np and VXi=npq…

Q: The random variable X takes value O with probability, and value 1 with the remaining probability.…

A: We have given information, The random variable X takes value 0 with probability 13, and 1 with…