Loss amount, X, follows a gamma distribution. You are given E[X] = 8, Var[X] = 32. Calculate the probability that the loss amount exceeds 3, P

Q: Under some circumstances the waiting time X for an event could be modeled with the following pdf:…

A: Given information: f(x)=θ801-x80θ-1, 0<x<80 Given θ=4 a. CDF of X: F(X)=∫0xf(t)dt…

Q: T has an exponential distribution such that P(T≤2)=2P(T>4) What is Var

A:

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: normal pdf.

A: For a normal distribution with parameters μ &σ the pdf is given by:

Q: 0, x< 0, F4(x) = |, x20. 1- 0.3e-0.00001z For the above model, determine the following: a. Mean…

A: Given  F4x=              0                   ,  x&lt;01-0.3e-0.00001x     ,  x≥0

Q: (a) Determine the pdf for X.

A:

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A: Single Exponential Smoothing: The formula for Exponential smoothing is,…

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A: Given: The cumulative probability distribution is shown below Flow (xn)  P (X&lt; xn) 0 0 25…

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A: The table lists future concentrations of a certain greenhouse gas in parts per billion (ppb), if…

Q: Let Xi take on an exponential distribution: f(x) = theta * exp(-theta*x). Show that the MLE for…

A: Solution

Q: In 2016, losses follow the distribution F(x) = 1- 0.3 .e -0.00001x x 2 0 There was uniform inflation…

A: Given  Fx=1-0.3e-0.00001x , x≥0      Inflation rate=1.50%         Deductible=3000

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A: Number of lung cancer cases occurring within the group are modeled using the function - N(t) =…

Q: We previously determined P(x ≤ 3) = 0.202. Use Table 2 to find the cumulative probability P(x ≤ 2)…

A: From the given information,Here, X follows Poisson distribution.

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A:

Q: 5) Consider the distribution of lifetimes, X(in months) of a particular type of component. The CDF…

A:

Q: X is exponentially distributed with a mean of unity. What is the pdf of Y=1-exp(-X)? Use the 440 40…

A: Given,

Q: Q3. Exponential Distribution has a memoryless property. Intuitively, it means that the probability…

A: Given : X~Exponential(λ) The pdf of X is  f(x)=λ×e-λ×x  ; x&gt;00              ; otherwise The cdf…

Q: -xª-1e¯×/Þ, if x > 0 The Gamma(a, B) distribution has pdf: f(x) = r(@)ßa* 0, 10. %3D otherwise…

A: Note that, here, β = 3 n samples, X1, X2, ..., Xn are collected from the distribution Gamma( α, 3)…

Q: Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

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A:

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A: It is an important part of statistics. It is widely used.

Q: Consider the function.   What is the approximate average rate of change of f(x)f(x) from x=0x=0 to…

A: Average rate of change is ratio of difference of f(x) to difference of x.

Q: Differentiate the function. A(s) 13 = - s6 A'(s) =

A:

Q: The (cumulative) distribution function of X is given below: 0 Fx(x)=¹ for { for for x 1. (a)…

A:

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!