Suppose that a random variable X has a continuous uniform distribution: S (x)= {/2, 4

Q: For a random sample Y1,..., Yn iid f (y; 0), define the following: - the likelihood function; | -…

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

Q: Let X = N(μ, A), where 2 3 -2 1 -0) --(9) -- (₁) and A = -2 20 1 02 Determine the conditional…

A: Let , where and

Q: 1- P(Y > 1) 2- P(X>2|Y< -1) 3- P (3<X<7)

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Q: Q1: Let x1, X2. .., Xn, Xn+1 be a random sample of size n + 1,n > 1, from a distribution that is…

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Q: Suppose X is a random variable with X - N(70,9²) and let H = the mean of X • me = the median of X •…

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Q: A random variable X has the following PMF: [refer to image] a) Find E(X) b) If Y = g(X) = X^2,…

A: The PMF of X is given as:

Q: la) P(X>2) (b) P (Y > 0), where Y = - 2

A: given  X~N5,2  the  z=X-μσ~N0, 1    mean = 5     variance = 2      ,   a) PX &gt;2=PX-μσ&gt;2-52…

Q: Mx Sb sa e -e (5)- s16-a) X~U(a,b) , Calculate the variance of the random variable X.

A: Given mgf of Uniform distribution function, we need to find Variance

Q: (a) p IX – 31 2 2 (b) p IX – 31 2 1

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Q: Q3: let x be random variable with Beta distribution, find the V(x)?

A: Beta Distribution: A continuous random variable X is said to follow Beta distribution with…

Q: Using Basu’s Theorem to show that for a random sample drawn from a normal distribution N (μ, σ2),…

A: It is given that a random sample from the Normal distribution N(μ,σ2).

Q: Suppose Y₁, Y2,,Y,, is an iid sample from a beta (a, 3) distribution with a 3-0, 0>0 a. Use the…

A: Given:Y1,Y2,.....,Yn is an iid sample from a Beta(α,ß)α=ß=θ,    θ&gt;0Find:a)Show that the given T…

Q: The weekly demand for propane gas (in 100's of gallons) from a particular facility is a random…

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Q: A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x-x²+4) =

A: Given that E(X) = 1.5, and var(X) = 0.25 The var(X) is defined as Var(X) = E(X2) - (E(X))2

Q: A size 2 sample will be selected without replacement of a population X with values (2 , 4, 6). Let…

A: Introduction: The population consists of the three numbers- 2, 4, and 6. A sample of size n = 2 is…

Q: (a) Let Z be a discrete random variable taking one of the four distributions covered in Chapter 10.…

A: Given that Let Z be a discrete random variable taking one of the four distributions covered in…

Q: f X is a uniformly distributed random varibale with a=9 and b=16, then Calculate the…

A: Answer: From the given data, X follows uniform distribution, a = 9   and   b = 16

Q: What is the distribution of X? 1) Out of the 38 pizzas that you try, how many would you expect to…

A: Let p be the probability of you liking the pizza. Given that p = 0.08

Q: EXERCISE 3 Let X1, ..., X, be independent exponential random variables with mean 1/ß. Find the…

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Q: Let x be a dis crete random variable with probability distribution fCx) =k (x² + 20) and x =…

A: i. From the given information, the probability distribution function is f(x) = K (X2 + 20) and x=…

Q: Random variables X and Y have the means and standard deviations as given in the table to the right…

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Q: Suppose that Y1,..., Yn is a sample of size n from a Exp(B), B > 0. .3B (a) Find the distribution of…

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Q: A random variable X has a normal distribution N(4,9). (1) Find V(X) and E(X²). (2) Let + be the cdf…

A: The normal distribution of the random variable is N(4,9).

Q: Let x be random variable with E(x) = 2 and var(x) = 3. Verify that random variable x and the random…

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Q: Suppose (X1, X2, ... , X12) is a random sample from Normal(u = 4, σ = 62). If we let x̄ be the…

A: From the given information,  It is provided that there are 12 random samples from the normal…

Q: If Y is a standard Cauchy random variable, show that Y and are identically distributed. Y

A: Solution

Q: Q9. For a portfolio of fully discrete 40-year endowment insurances of 1 on independent lives age x,…

A: We have consider S as the aggregate loss random variable and L as loss at issue random variableHere…

Q: The probability that a sample variance of size 11 taken randomly from a normally distributed…

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Q: Inspection trials are carried out in a factory to assess the quality of products. In each trial r,…

A: Given that  be the number of satisfactory items in the trial and is assumed to follow the binomial…

Q: (a) (b) Find E(W). Find Var(W).

A: Given,let  be  independent random variables.E(Yi)=μ and Var(Yi)=σ2  for every since (a)we want to…

Q: Soalan/ Question 2: Given a normally distributed population with a mean of 75 and a variance of 625,…

A: Given that mean =75 , variance = 625

Q: Q2/ Let X be a random variable with normal distribution N(0,4) and Y=(X+2)² find:- 1- P(Y > 1) 2-…

A: 2) Given Y=(X+2)2, we want to find the probability that Y is greater than 1 . This is equivalent to…

Q: For a discrete random variable X if : Points ) P ( X = x ) = 0.1x , x = 2 , 3 , 5 , then E ( X2 ) =

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Q: The continuous random variable T represents the time in hours that students spend on homework. The…

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Q: Suppose that X1, X2,..., X, constitute a random sample from a uniform distribution in the interval…

A: Given: X1, X2,......,Xn constitute a random sample from a uniform distribution in the interval…

Q: Suppose X has a continuous uniform distribution over the interval -1,1. Determine the variance.…

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Q: Using the pdf file f (x) x | A; Find the expected value and the variance of the random variable Y,…

A: Expected value of X is given by E(x)= integration|x x*f(x)dx = Integration|0.450.75 2.123(x-x3)dx =…

Q: Calculate the Average and the variance

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Q: If X is a uniformly distributed random varibale with a=8 and b=13, then Calculate the mean…

A: Answer: From the given data, X follows uniform distribution, a = 8  and  b = 13

Q: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. .…

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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!