Show that if a random variable has an exponentialdensity with the parameter θ, the probability that it willtake on a value less than −θ · ln(1 − p) is equal to p for 0 Fp < 1.

Q: The log-likelihood  can be expressed as: There are two Sigmas, are they read a the Sum of sum or is…

A: The log-likelihood  can be expressed as:There are two Sigmas, are they read as the Sum of sum or is…

Q: Accidents occur at a rate of 2.5 per month, and the time between accidents is exponentially…

A: Hi! Thank you for the question As per the honor code, We’ll answer the first question since the…

Q: 4) Find the indicated probabilities, given that the lifetime of a lightbulb is exponentially…

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Q: The manager wants to know whether the true average number of power tools rented/day is 25.0. If in a…

A: Given : Ho: σ = 8.9 rental against HA: σ &lt; 8.9

Q: The integral equation for a normal distribution curve's probability A. is an example of a…

A: Normal distribution curve's probability :- Normal distribution fits many natural phenomina  as Blood…

Q: If X has a exponential distribution with parameter 2,find the p.d.f of Y=log X.

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Q: Find the required probabilities using the exponential density function RE), (0.-). The time t (in…

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Q: Q 3. A random sample X, X2, .., Xa is drawn from a population with pdf f(x,@) = (1+ 0 x), -1<x <1,…

A: Consistency: Let Tn be a sequence of estimators such that for all  θ∈H  ETn→γθ ; n→∞VTn→0 as n→∞…

Q: At time t= 0, 11 identical components are tested. The lifetime distribution of each is exponential…

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Q: = 6. The lifetime, in years, of an air compressor is an exponentially distributed random variable T…

A: Given: If compressor is defective, the lifetime Td has mean μ=0.1 If compressor is not defective ,…

Q: Suppose that X has a lognormal distribution with parameters e = 5 and w? = 9. Determine the…

A: Solution-: Given: θ=5,ω2=9 ∴ ω=3 We find x such that, P(X≤x)=0.95

Q: (i) IfX is a normal RV with mean zero and variance o, find the pdf of Y = e*. (ii) If X has an…

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Q: Problem 10 ) Suppose that battery failure time measured in hours has a probability density function…

A: Given information: The probability density function fx=2(x+1)3.

Q: 1. SupposeX1,..., Xniid∼Exponential(λ) is a set of n observations drawn independently from an…

A: We have given that, X1, X2, . . . . .  . . .  , Xn iid ~ Exp( λ ). The pdf of exponential…

Q: Y is an exponential random variable uith var [y]<25 what i's the PDr of y? what is the ELY]? what is

A: Given that Y is an exponential random variable. And, varY=25 Exponential distribution: A random…

Q: You are given: 1. Losses follow a lognormal distribution. 2. E [X] = 1.5296 3. Var [X]=0.6645…

A: Step 1: Identify the Mean and Variance of the Log-transformed Variable Y. We are given:…

Q: A RV X is exponentially distributed with parameter 1. Use Tchebycheff's inequality to show that P(-1…

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Q: If X has Exponential Distribution with parameter 1,find the p.d.f of Y = √√x.

A: Given  X~exp(1)

Q: Show that if the exponentially decreasing function if x 0 f(x) = LAe is a probability density…

A: Given: fx=0              ;  if x&lt;0Ae-cx     ;  if x≥0 For a probability density function f(x).…

Q: What is the mean (E[X]) of the following statistical function? f(x)=c*(x)^9 from 0 to 9 and f(x)=0…

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Q: Let X denote the distance (in meters) that an animal moves from its birth site to the territory…

A: Given : X follows exponential distribution with parameter μ=0.0015 Mean : E(x)=1μ        =10.0015…

Q: Let U1, . . . , Un be a random sample from the Unif(0,1) distribution. (a) Find the distribution…

A: U1,U2,...,Un is a random sample from U(0,1).The PDF of U is given by:f(u)=1;0&lt;u&lt;1

Q: At time t = 0, 19 identical components are tested. The lifetime distribution of each is exponential…

A: From given data we have : Y=11 n=19 so, p^=Yn   =1119

Q: Experiment X is consist of drawing two balls from a basket containing 13 blue and 5 red balls.…

A: Solution: From the given information, a basket contains 13 blue and 5 red balls. Total number of…

Q: Let U1, . . . , Un be a random sample from the Unif(0,1) distribution. (a) Find the distribution of…

A: The objective of the question is to find the distribution of a transformed random variable and to…

Q: Consider an exponential model for car crashing. Let T be the time in days between the beginning of…

A: Introduction:The cdf of an exponentially distributed random variable, T with the given pdf is F (t)…

Q: The value for x such that P(X S x) = 0.95]

A: Here given  X has lognormal distribution with theta = 5 And Variance = 9 So standard deviation  = 3

Q: 3. Suppose a random variable X has pdf given by f(x) = |cos(x)1/4 for n/2 sx s 5n/2. Find the median…

A: To find median we use the formula, Integration|xM f(x)dx = 1/2 Where M is median

Q: n x² = Σ i=1 (O₁ - E₁)² Ei Prove that the above statistic follows a chi-square distribution with al…

A: Solution-: We want to prove  χ2=∑i=1k(Oi-Ei)2Ei with determination of degree of freedom

Q: suppose that the lifetime of a light bulb is exponentially distributed with mean 2 years. what is…

A: Let X=the lifetime of a light bulb Given that X follows an exponential distribution with mean=2 So,…

Q: For this prediction model, what is the probability of reaching the target from a distance of 49…

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

A: *Answer:  306 answers X~Exponential with mean

Q: The Exponential pdf for continuous random variable Y takes the form e/ß y > 0 fV) = for ß > 0. y < 0…

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Q: Need within 1 hour please... A lottery offers INR 1000 with probability 0.25, INR 16 with…

A: Given Information: The utility function is,    u(x)=log(x) The table that shows the outcome with…

Q: Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter…

A: X1,X2,...,Xn is a random sample form X∼Beta(θ,1). The PDF of X is give…

Q: ake the derivative of f(x) = lae-lxxa-1 with respect to x and set the derivative equal to 0.  This…

A: f(x)=lae-lxxa-1 where l and a are positive constants. Lets use product and chain rule. Product rule…

Q: For a fully discrete whole life insurance of 100,000 on each of 10,000 indepen- dent lives age 60,…

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Q: 22-Suppose that X X, form a random sample from a beta distribution with parameters a and 8, where…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.