Calculate the variance of a random variable X whose characteristic function is (1+ e3it)² f(t) = 4

Q: The input voltage to a rectifier is the continuous uniform (-1, 1) random variable U. The rectifier…

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Q: Company A claims that the variance of the life of its appliances is less than the variance of the…

A: Company A claims that the variance of the life of its appliances is less than the variance of the…

Q: The hospital period, in days, for patients following treatment for a certain type of kidney disorder…

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Q: generating function M,(t) = 2 determine the 2-t variance of X.

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Q: "What is the correlation coefficient for this condition? X is the voltage across a resistor, Y is…

A: We have given that the statement about to the correlation condition of X and Y.   Note: According to…

Q: Show that the mean of a random sample of size n from an exponential population is a minimum variance…

A: Let X1, X2, …, Xn denote random sample from exponential distribution with θ. The probability density…

Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is…

A: The mean is calculated as follows: EI=∑I×PI=1×p+0×1-p=p

Q: let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance…

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Q: Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2…

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Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: X and Y are independent. If we are given P(X = 0) = P(X =1) = P(X =2) = }, P(Y = 1) = 3. P(Y = 2) =…

A: The question is simple and formula based, we need to know the mathematical formulas which are used…

Q: (a)Find the probability that the selected bulb can survive for at least 3 years. (b)Find the…

A: Given,there are 5 types of bulbs.the lifetime of a bulb of type n follows an exponential…

Q: Show that the characteristic function of a Gaussian random variable with zero mean and variance o2…

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Q: how that the variance of a geometric random variable X; is given by V ar(X) = q/p^2 .

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Q: The hospital period, in days, for patients following treatment for a certain type of kidney disorder…

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Q: Derive that the variance of the forecasted error using Exponential Smoothing (ES) method is given by…

A: Given the variance of the forecasted error using the Exponential Smoothing (ES) method as

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: Prove that the variance of a beta-distributed random variable with parameters a and 3 is αβ (a + B)²…

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Q: If a random variable X has the moment generating function Mx (t) = 2 - ť Datermine the variance of…

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Q: If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.

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Q: Example 24: If a random variable X has the moment generating function Mx (t) = 2-t' 2 determine the…

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Q: Show that the mean of a random sample of size n from an exponential population is a minimum variance…

A: Show that the mean  of the random sample of size n from an exponential population is a minimum…

Q: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the…

A: The given pdf is shown below:

Q: Without using a moment generating function; Prove that the variance of a beta-distributed random…

A: Let X be a continuous random variable that follows a Beta distribution with parameters α and β.The…

Q: In a poisson distribution P(X=0)=P(X=2).Find the variance V(X) of X.

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Q: Show that variance o? (x²) – ((x))²

A: Solution

Q: In a large lot of manufactured items, 10% contain exactly one defect and 5% contain more than one…

A: For Y1 : Since each items are interdependent so Y1~Bin(10,0.1)  For Y2 : Since each items are…