Q.#4 (a) If X has a Uniform Distribution in (-a, a), a > 0, find a such that P(|X| < 1) = P(|X| > 1). Also find P(]X – 1| < 2) and P(|X|> 2).

Q: (A)- If x ~ EXP(A) and let A~EXP(m). 1- find compound exponetial - exponetial distribution 2- find…

A: Given that x~exp(λ) and λ~exp(m) distributions. Compound distribution is a form of marginal…

Q: Let X and Y be independent v.a with uniform distribution on the interval (0, 20) and (0, 30)…

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Q: Let Y have a truncated distribution with pdf g(y) = φ(y)/[Φ(b)−Φ(a)],for a &lt; y &lt; b, zero…

A:

Q: Let X1, . . . , Xn, . . . ∼ iid Poisson(λ). (a) Using the Central Limit Theorem, find a limiting…

A: According to the central limit theorem, as long as the sample size is large the sampling…

Q: Assume that X has the distribution N (10, 4), find:   P (Z > - 3)     P (11.36 < X < 16)

A: From the provided information, Mean (µ) = 10 Standard deviation (σ) = 4 X~N (10, 4)

Q: f(x) = c/x with x = 1,2,3. Given the Geometric Distribution find M(t).

A: Given, fx=cx,x=1,2,3 Consider,         ∑fx=1          ∑cx=1c1+c2+c3=1   c(1.8333)=1…

Q: distribution is given as X ~ U(0, 12). Find P(x > 3)

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Q: Let X has uniform distribution on [-1,1]. Find E(X|X²).

A: Given: X has uniform distribution on [-1,1]. Then the pdf is: f (x)=12for -1&lt;X&lt;10Otherwise

Q: 3. Assume that an insurance company will experience a loss X that is modeled by a uniform…

A: Given,A random varible X~U[2,10]f(x)=110-2f(x)=18 ; 2≤x≤10

Q: Let F(x) is distribution function then P(a <x sb)=F(b) – F(a) صواب

A: For a continuous random variable XX, once we know its cdf FX(x)FX(x), we can find the probability…

Q: Certain small toys are advertised to weigh 28 grams. However, the actual distribution of weights can…

A:

Q: 6. Given a continuous uniform distribution, show that A+B (a) μ = and 2 (b) 02: (B-A)² = 12

A: The objective of this question is to derive the formulas for the mean (μ) and variance (σ²) of a…

Q: Let X have a distribution N(2,4). Calculate P(|x| =<1.2) and P(|x| =<11.6) and determine such x for…

A: Given: Let X have a distribution N(2,4) =&gt; μ = 2 σ2 = 4  =&gt; σ = 2

Q: The distribution of X, the time it takes women between 50 and 55 to run a 10k race, is such that the…

A: It is given that:

Q: If X has a Uniform distribution on the interval of [o, 20], then what is P(X+84/X 2 19)? Select one:…

A:

Q: Let F be a distribution function on the line with only two discontinuities at 1.2 and -1.4 with…

A: From the given information, Consider, F be a distribution function on the line and it has been…

Q: Suppose that X is normally distributed with u = 10 ando 2. Find P(IX 10|S3)

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Q: A RV X has a uniform distribution over (-4, 4) compute P(|X|>2)

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Q: Does a distribution exist for which: Mx(t) = (t)/(t-1) for |t| < 1? If yes, find it, otherwise prove…

A: Given the distribution function,  Mx(t) = (t)/(t-1) for t &lt; 1

Q: If X has a Uniform distribution on the interval of [0, 15], then what is P(X+15/X > 8)? Select one:…

A: Answer:

Q: A distribution is given as X ~ U(0, 15). Find P(x < 4) and round to the nearest hundredths place.…

A: It is given that the X~U(0,15).

Q: Assume that X follows a continuous uniform distribution on the interval [3, 8]. Find P[X s 6].

A:

Q: Let X N(0, 1), and let Z ~ Unif{-1, 1} (i.e. P(Z = −1) = P(Z = 1) = 1/2) be independent of X. Let…

A: It is given that X~N0,1 and Z=-1       p=0.51          p=0.5 X and Z are independent.

Q: Suppose X has a continuous uniform distribution over the interval [-5, 5]. Determine the following:…

A: Solution: From the given information, X follows uniform distribution with parameters a=–5 and b=5.

Q: Let m|q0 denotes the probability that an individual who survives at the initial time t=0 will die…

A: we will provide the solution of all 3 parts

Q: Let (X1, ., Xn) be a random sample from the following discrete distribution: 2(1 – 0) P(X1 = 1) =…

A:

Q: Q5: suppose that R is the range of a random sample of size 4 from a population = ] with Uniform…

A: Let,  is the range of the random sample of size .The sample is collected from the population with a…

Q: et X1,..., Xn be a random sample from a uniform distribution on the interval [20,0], where 0. et…

A: Solution

Q: If F(x) is the CDF of the standard normal distribution Z~Norm(0,1), show that (a) For 0 ≤ a &lt; b,…

A: (a)From the given information, F(X) is the CDF of the standard normal distribution.

Q: (+12 If X has a uniform distribution on the interval from 0 to 10, then what is P(X + 7) ? IV

A:

Q: If X has a Uniform distribution on the interval of [0, 20], then what is P(X+84/X> 19)? Select one:…

A:

Q: A. Find the value of k such that: P(Z>k)=0.25 B. Let F(6,9) denote a random variable having an F…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Continuous variable X is uniformly distributed on the interval [7.5, 32.6]. What is its interquartil

A: Given that X is uniformly distributed on the interval [7.5, 32.6]. fx=132.6-7.5      =125.1,…

Q: x has the uniform distribution [0,1] put y=2x + 5 then y has the uniform distribution on the…

A:

Q: O Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is…

A: The following solution is provided below:

Q: Pind the values of the constants a' and 'b' such that the CDF Кx (х) %3D 1- а.е xb] и (х) is a valid…

A:

Q: If Xhas the Poisson distribution with P(X=1) = 2P(X=2), then P(X ≥ 2) is approximately

A: The probability mass function for Poisson random variable X is, Given that P(X=1)=2P(X=2).

Q: IfX is a RV with a continuous dištribution function F(x), prove that Y = F(X) has a uniform…

A:

Q: Let X have a uniform distribution on the interval [0,1] and let Y ~ N(0,1). Suppose that X and Y are…

A: Here, X ~ Uniform(0,1) Y ~ N(0,1) PDF of X, fXx = 1if 0&lt;x&lt;10otherwise So, CDF of X, FX(x) =…

Q: Determine whether the following is a valid distribution function

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.