If X has the exponential distribution given by f(x) =0.5 e−0.5x, x > 0, find the probability that x > 1.

Q: Suppose the probability density function of a random variable X is given by f(x) = e-(x-2)² - co <x<…

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Q: The random variable X has the following probability density function:  fX(x)={9xe−3x 0≤x<∞ 0…

A: Given,f(x)=9xe-3x     ; 0≤x≤∞0              ; elsewhere

Q: For the continuous probability function f(x) = 2kx? e-* when x 2 0. Find a. value of k %3D b. mean

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Q: For c in R, calculate E[e^cX] where X is exponential distribution.

A: In question, We'll find the E(e^cx) that is mgf of X, where X from exponential distribution. The…

Q: Given is the following probability density function f(x) = e*; x > 0 The expected value of y=e3/4x…

A: Probability Density Function: A continuous function f(x) is said to be the probability density…

Q: Let X, and X, be random samples taken from the exponential distributionf (x) = 4e¬4x, 0<x<∞. a) Find…

A: The PDF of the exponential distribution is given by, f(x) = 4e-4x , 0&lt;x&lt;∞ X ~ Exp(4) So, E(X)…

Q: . If X is an exponential random variable with parameter B = 1, find the probability density function…

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Q: For the continuous probability function f(x) = 2kx² e¬* when x > 0 a. value of k %3D b. mean

A: Integration of continuous random variable is 1.

Q: Complete this PDF and find the expected value of X:

A: The P(x) for X = 2 is calculated as follows: PX=2=1-0.3+0.2+0.4               =1-0.9…

Q: (c) If x is a value of a r.v. X having an exponential distribution with mean 0, find the constant c…

A: Let X be a random variable having an exponential distribution So, 0&lt;x &lt; cx is a (1-α) 100%…

Q: A fire service response team always reaches the scene of an accident within 6 minutes. The time Y in…

A: Given, A fire services response team always reaches the scene of an accident within 6 minutes. The…

Q: The time untila chemical reaction is complete (in milliseconds) is approximated by the cumulative…

A: Here given CDF  F(x)= 1-e-0.01x, x≥0

Q: (a) the joint probability function f(x, y),

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Q: From this density, the probability that X > 1.02 or X < 0.32 is:

A: The probability distribution of X is  f(x) = 12  ; 0&lt; x&lt;2

Q: Given the probability density function as below (hx² f(x) =} (-15xs 1) otherwise

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Q: Given the probability density function f(x) = }x over [1, 3], find each of the following. 15. E(x)…

A: Given the probability density function  fx=14x     ;0≤x≤3 15. We need to find E(X). Formula for E(X)…

Q: X has an exponential distribution with λ=2. Calculate the following The value of x such that…

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Q: If X has the exponential distribution given by: f(x) = 4*(1 - x/2); 1 ≤ x ≤ 2.   Find the…

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Q: (4x³ : - Suppose X has probability density function Jx(x)={ 0<x<1. : otherwise

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Q: IF X has an exponential distribution with the parameter 0 and Hx = 20, where 0>0 then P(X > 1) is:…

A: We know that :  For exponential distribution, the mean is equal to the standard deviation; i.e., μ =…

Q: Suppose Ilhan's utility function is U+0.5*Y^1/2, Ilhan's income is $125,000 when healthy but only…

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Q: The random variable is said to follow the distribution of Benford’s Law if P(X=i)=log10(1+i)/i…

A: The given probability mass function is as follows:

Q: The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately…

A: For a continuous random variable X, which follows exponential distribution, the probability density…

Q: i. Find E(T). You can use the mean of an exponential distribution without proof, but you need to…

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Q: Suppose that X has a lognormal distribution with parameters 0 = 5 and w2 = 9. Determine the…

A: We have given that,  Let X be the random variable from Log normal distribution with parameters θ = 5…

Q: The digestion time in hours of a fixed amount of food is exponentially distributed with average 45…

A: The exponential distribution is the continuous distribution which is defined for the time between…

Q: Find Prob(3 < x < 7) given that the probability density function is f(x) = .2e:2ª,

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Q: The ratio of selling prices of a security on consecutive days has a lognormal distribution with…

A: From the information, we have  μ=0.02σ=0.06x=1,5 Therefore, for Lognormal distribution probability…

Q: If the cumulative distribution [Q5B] function of f(x) is F(x), find: E(X) 1- e-8x x > 0 F(x) =…

A: Cumulative function of  fx is given as follow: Fx:1-e-8x     x≥00              otherwise We need to…

Q: The time a postal clerk spends with his or her customer has an exponential distribution with a mean…

A: In question, We have given that amount of time is following exponential distribution with mean 4…

Q: Suppose that the length of long distance phone calls, measured in minutes, is known to have an…

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Q: Suppose the survival function of the curtate lifetime of a newborn baby is given by 100 – x s(x) = =…

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Q: For a particular kind of battery, the probability density function for x hours to be the life of a…

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Q: If X ~ U(3, 15), what is the probability density function for this distribution?

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Q: Find the method of moments estimator for the parameters of the double exponential distribution DE(0,…

A: the answer is in the image uploaded below

Q: Suppose that the length of long distance phone calls, measured in minutes, is known to have an…

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Q: Suppose that the life distribution of an item has the hazard rate function 1(t) = t³,t > 0. What is…

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Q: (f) For each of the following families of distributions, explain whether it is an exponential…

A: One parameter exponential family of distributions can be expressed as, f(x|θ) = h(x).exp[u(θ).T(x) -…

Q: mean(log X)= 3.4, Sjogx = 0.136 and k=1.2, using the log Pearson Type III distribution. The…

A: Option A

Q: Find the conditional probability density function of Y given X? pte: If the answer is (9+1) write it…

A: Solution

Q: Given the following probability density function: f(x) = 6x(1 – x) 0 < x < 1 Find E(X2).

A: From the given information, fx=6x1-x, 0&lt;x&lt;1

Q: Suppose that X is the length of time (in minutes) that a customer queues in a bank. The probability…

A: Given,fX(x)=(36-x2)144    ;  0≤x≤60                 ; otherwise

Q: Q2. If x is a value of a r.v. X having an exponential distribution with mean 0, find the constant c…

A: The given interval is 0 to cx is a 1001-α% C.I. for the parameter θ. Calculate the value of c.

Q: A random variable T(x) has a distribution function that 0 <t< 100 – x defined by Fr(2) (t) = {100-x'…

A: From the given information, FTxt=t100-x, 0≤t≤100-x1               t≥100-x Consider, the density…

Q: 2. Suppose that the cumulative distribution function of the lifetime of a piece of operating…

A: Let f(t) be the probability distribution function and F(t) be the cumulative distribution function…

Q: Suppose that x has an exponential distribution with θ =1.5. Find P(x > 1

A: The probability distribution is given by: f(x) =1.5e(-1.5x)    for x&gt;0

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!