A geometric random variable X is a discrete variable taking values in {1, 2,...} with the parameter p which models the probability of getting the first success on the nth trial. This variable has density function fx(x) = p(1 – p)ª-1. Find the moment generating function of X and | use it to find the mean and variance of X.

Q: choose the correct statement for the first order stationary random process X(ts): O a the PDF…

A: A random process {X)(t),t∈J}  is stationary if the statistical properties do not change by time.

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: Find the PSD of a stationary random process for which Auto correlation is RYx (t) 6 e- alt|

A:

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: Find the characteristic function of the geometric distribution given by P(X = r) = q' p, r = 0, 1,…

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Q: Suppose X is a random variable taking values in the interval [0,2] with probability density function…

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Q: Normal distribution.   The moment generating function of a random variable U is M(t) = (1 -…

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Q: Let fx (2) be the probability density function of the random variable X. 3 f(2) =10, 2 28 -1<z<3;…

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Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34.…

A: Formula used Var ( X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

Q: If the probability density of X is given by f(x) =2x−3 for x &gt; 10 elsewherecheck whether its mean…

A: Solution: From the given information, the probability density function of X is

Q: (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X.

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Q: Let X and Y be two random variables with joint probability mass function: p(x,y) = 1/48 xy(1+y) ???…

A: The provided joint probability mass function is:

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

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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: 36. QUESTION: Let X have the density f(x) = 2x if 0 < r <1 and f(x) = 0 otherwise. Show that X has…

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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…

A:

Q: 5.5.4. Let Y1, Y2, ..., Yn be a random sample from the uniform pdf fy(y; 0) = 1/0, 0 ≤ y ≤ 0.…

A: Step 1: Step 2: Step 3: Step 4:

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: If a dealer’s profit, in units of $5000, on a new automobile can be looked upon as a random variable…

A: The E(X) is calculated as follows: E(X)=2∫01x(1-x)dx=2∫01(x-x2)dx=2(x22-x33)01 =2(12-13)=13

Q: False

A: Random Process: A random process is a stochastic process. It is denoted by X(t) that is the value of…

Q: (Y-1)². Use one decimal place accuracy.

A: Given that  Y ~ Uniform (1 , 11)

Q: distributions of both Y1 and Yn are uniform and continuous

A: We know that first order statistic PDF is given by fy1(y1) as shown below. Mean or Expected value…

Q: continuous random variables Z is known to have an Erlang (2,1.3) type PDF. what is the variance of Z

A: Given that Z is a continuous random variable having a distribution Erlang with parameters (…

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

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Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is…

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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 probability distribution of the discrete random variable X is 3-x x = 0,1,2,3. .4, Find the…

A: Solution-: We have the p.m.f. of X is given by,  f(x)=3x*(14)x*(34)3-x f  ;  x=0,1,2,3;   We find…

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: Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1.  Calculate the mean(x)

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: The time to wait between each phonecall a person recives is random given f(t) = 3e-3t for t>=0. Let…

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Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

A: From the given information, the joint density function for X  and Y is,

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!