There are thirty Exam P takers at a certain testing center. The probability of failing the exam is 40%. Students are assumed to pass or fail independently of each other. What is the expected number of failures, E[X], and the variance, Var[X]?

Q: Let X1, X2, X3, X4 be a random sample from the distribution with PDF f(x) = e¯, x > 0. Calculate the…

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Q: If the probability density function of the random variable X is x>0, f(x)= 0, Otherwise. Then the…

A: Given data :  f(x)=e-x , x>0 0 , otherwise Finding Mean ,…

Q: Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an…

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Q: Let X be a random Vaviable with the Following pdf FX) s Oo20, x=5,10,15,2025 %3D elsewhere. then the…

A: The formula for variance is given below: VX=EX2-EX2 Here, EX2 is the expectation of random variable…

Q: Consider an exponential distribution with parameter 3 > 0, ie., its pdf is f(x|3)==-e-/8 if x ≥ 0. е…

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Q: Let X be a continuous random variable with PDF 2x 0 < x < 1 fx(x) = {0 otherwise Find the expected…

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Q: The PDF of random variable x is given as, [0.3507 Vx, 0<x<3 1,(x) = 0, otherwise Find the, (1) (ii)…

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Q: Let X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.

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Q: A pumping station operator observes that the demand for water at a certain hour of the day can be…

A: The objective is to find out the max. capacity of water when demand follows exp. dist. with mean…

Q: For every a, 0 > 0. i) Derive the expected value of X. i) Derive the variance of X.

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Q: Find the probability that the range of a random sample of size 4 from theuniform distribution having…

A: Given: Sample size, n=4 f(x)=1,   0&lt;x&lt;1

Q: A random variable X has the following pdf: f(x) = 9xe-3"; x > 0

A: Given: random variable x with gamma distribution with pdf  f(x)=9*x *e^-(3x)  : x&gt;0  then to find…

Q: Find the mean of the random variable X with PDF S 3x² _if 0 <x < 1, f(x) = otherwise.

A: For the given random variable X, its pdf is

Q: The PDF of random variable x is given as, 0.3507 Jx, 0<x<3 1,(x): 0, otherwise Find the, Mean

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Q: 2. Suppose X has the normal distribution with parameters u and o2, fin the E(e2X).

A: x follow s normal distribution with mean x and variance sigma sqaure.  By using moment generating…

Q: For continuous random variable X with f(x) as its pdf, the cdf is f (u) du O True O False

A: We want to tell you above statement is true or false

Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: We want find  Mean= E(x) , variance = var(x)

Q: Let X be the total medical expenses (in 1000s of dollars) incurred by a particular individual during…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: Suppose that X1 and X2 are independent and exponentially distributed random vari- Let Y1 = X1 + X2…

A: It is given that X1 and X2 follows Exponential with parameter λ. We will use Jacobian method of…

Q: Suppose that the Cumulative distribution function (CDF) of the random variable X with parameter 0 >…

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Q: Find the mean of the random variable X with PDF S 32² if 0 <x < 1, otherwise. f(x) =

A: Given : The probability distribution  function f(x) To find : Mean of the  random variable X

Q: 0<x<1 f (x) = {2-x 1<x<2 18x<2 otherwise

A: Chebyshev’s theorem = P (|x - μ| ≤k2 ) ≥1-1k2

Q: If E denotes the expectation the variance of a (random variable X is denoted as (E(X))^2 - E(X

A: Given: If E be the expectations then varience of random variable x  Var(x)= (E(x))^2-E(x)  a); True…

Q: The CDF of a continuous random variable X is F(x) = 1 - e-/5. Then the pdf of X is

A: We have given that, CDF F(x) = 1 -e-x/5 The pdf is given as f(x)= d/dx( F(x))

Q: 1. Let X be a random variable with probability density function f(x) = {k(4 – x²) -2<x<2 otherwise…

A: #1     X   be a random variable with pdf                      f(x)  = k(4-x2)      -2 &lt; x &lt; 20…

Q: Let Y be a random variable with pdf giyen by

A: Given that fy=30y21-y2, 0&lt;y&lt;1 Formula for Ey4 is, Ey4=∫01y4fydy

Q: The probability that a Poisson variate X takes a positive alue is 1- e-1.5. Find the variance and…

A: Given a Poisson variate takes positive values with probability 1-e-1.5

Q: Suppose that the unknown X is uniformly distributed between 0 and 1.  What is the expected value of…

A: Given: X is distributed uniformly between 0 and 1 a=0 and b=1

Q: In a certain city, the daily consumption of water (in million liters) approximately follows a gamma…

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Q: Let X be a random variable with E[X]=2, Var(X)= 4. Compute the expectation and variance of 3– 2X .

A: Solution-: Given: E(X)=2, Var(X)=4 Our aim to find, (a) E(3-2X)=? and  (b) Var(3-2X)=?

Q: A train’s arrival time at the station is T minutes past noon, where the PDF of T is given below.…

A: 12:05 means T=5  12:10 means T=10   We have to find the probability that the train arrives by 12:10…

Q: If a continuous RVX (> 0) possesses memoryless property, that is P(X>x+h)= P(X > x). P(X > h), then…

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Q: Let the probability function of the random variable X be defined as f(x)=cx^4 for x > 1, otherwise…

A: let the probabilty function is ,f(x)=Cx4      x&gt;1             0         otherwise

Q: 30. If e1+81' is the moment generating function of a normal variate X, find P(-1< X <9).

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Q: 4) What is the maximum likelihood estimator l for the Normal distribution, assuming o is known? The…

A: From the given information, fx=2πσ2-12e-x-μ22σ2 Consider, the likelihood function, L=∏i=1nfxi…

Q: X and Y are independent random variables, each exponentially distributed with a mean of Find P{X >…

A: GivenTwo exponential distributions X, Y with mean 110 I exponential distribution Mean =1λ=110⇒λ=10So…

Q: Consider the distribution of Binomial, Poisson, Exponential, Gamma, and let T=X+ 4 & T, = (X- 1).…

A: An estimator is said to be unbiased if E(Statistic)= Parameter If not so  Then the estimator is…

Q: Q1. A random variable is defined as “ the number of heads when             a coin tossed”,…

A: Let there are n trials and each having two outcomes - Success and Failure. The trials are…

Q: x f(x) 20 0.10 25 0.20 30 0.25 35 0.15 40 0.10 a. What is the probability that the firm will obtain…

A: Given data is x f(x) 20 0.10 25 0.20 30 0.25 35 0.15 40 0.10

Q: If X is normally distributed with mean 0 and variance 1, what is the probability density function of…

A: Solution: From the given information, X follows normal distribution with mean µ=0 and variance σ2=1.…

Q: Suppose that the unknown X is uniformly distributed between 0 and 2. What is the expected value of…

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Q: Consider the distribution of Binomial, Poisson, Exponential, Gamma, and let T1=X+4 and T2=(X-1)…

A: Let X be the random variable. Given that the statistic T1=X+4 and T2=(X-1). Unbiasedness: For a…

Q: Compute the standard score (Z-score) for x, when x = 21, the mean of the distribution = 27, and the…

A: Given that,X = 21Mean = 27Variance = 9

Q: Q1. If Var(X)=3, what is Var(2X + 1)? Q2. Compute the variance for a uniform random variable with a…

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Q: In the daily production of a certain kind of rope, the number of defects per foot given by Y is…

A: It is given that the mean of λ is 3.

Q: Find the marginal probability of X = 1.

A: Given:     Y     1 2 3 X 1 0.05 0.05 0 2 0.05 0.1 0.2 3 0.1 0.35 0.1

Q: If the random variable X has the rectangular distribution over (0,1) show that the MGF of the random…

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