If X has p.d.f. f(x) = .0sxs3 1o, 0.w. The probability that the quadratic equation 4t2 + 4tX + X +2 = 0 has real

Q: Suppose f(x) is pdf and is the mean of the random variable, then |(x – 4° f (x) dx = / x²f (x) dx –…

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Q: dy will be dx In x+1 If y = then 2x3 - 3x' (2x- 3x) +1)- (In x+ 1)(6x? – 3) (2x – 3x)? A. (2x - 3x)…

A: To find the dy/dx of the given function

Q: An insurer has data on losses for four policyholders for 7 years. The loss from the fh policyholder…

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Q: Amanda has a von Neumann-Morgenstern utility function given by U= VM , where Mis her income. If she…

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Q: Ann is a risk averse individual with the utility function u(w) = w1/2. Her current wealth is $300…

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Q: Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have…

A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: X is a continuous random variable having p.d.f. f(x) such that f(x) = kx2 Osxs5 otherwise Find : (a)…

A: According to our guidelines we can supported to answer only first three subparts   Given

Q: (2) The two basic SDEs. Solve the following SDEs and find the expectation and variance of X4. (i)…

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Q: 2. Under H, the likelihood function is given by L(1µ, a7) : A. True B. False

A: A random variable Y is said to follow the normal distribution with mean μ and variance σ2 if its…

Q: 3t For a random variable X with mgf Mx(t) = exp{t² – }; Find E[X²]

A: Given, MXt=expt2-3t2 Now, ddtMxt=ddtexpt2-3t2=expt2-3t2×ddtt2-3t2=expt2-3t2×2t-32=expt2-3t2×4t-32…

Q: Suppose we have the quadratic function f(x)=A(x^2)+2X+C where the random variables A and C have…

A: Let the quadratic equation is f(x)=Ax2+2X+C. From the question, f(A)=A2     0≤A≤2 f(C)=3C2    0≤C≤1…

Q: 0, elsewhere. Find the expected value and the covariance of g(X) = 4X + 3. %3D

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Q: If a is uniformly distributed over [-18, 30], what is the probability that the roots of the equation…

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Q: Consider: f(x, y) = 6x²y,0 < x < 1,0 < y < 1. The probability Pr(-0.5 < x < -1,0 < y < 1) is equal…

A: We want to find the probability

Q: Find Pr (0 < X1 <1/3,0 < X2 < ½) if the random variables X1and X2have the joint p.d.f. S(X1, X2) =…

A: From the given information, fx1, x2=4X1(!-X2), 0&lt;X1&lt;1, 0&lt;X2&lt;1 Consider, P0&lt;X1&lt;1/3,…

Q: The probability that x lies between a and b is given by P( a</= x</= b) =Sba f(x) DX. Given f(x) =…

A: A simple comparison gives, a = 1, b = 4, f(x) = x3/5000(10-x) = (10x3 - x4)/5000

Q: Let X ~ Exp(2). Find a real number a E [0, 1] such that the events {X € [0, 1]} and {X € [a, 2]} are…

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Q: The probability that X lies between a and b is given by P (a < X < b) = f(x)dx. Given f (x) = (10 –…

A: Simple comparison gives, a 1, b = 4, f(x) = x3(10 - x)/5000 = (10x3 - x4)/5000

Q: Find extreme value(s) of z = 2x¡ + x,xX2 + 4x3 + x,x2 + x} + 2

A: Consider the provided question, According to you we need to solve only part (d). (d)

Q: a) X, is Gaussian with a mean of0.5 dolai 6) X, -2 dolars with pnbabibidty os, with probalai litty…

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Q: Given discrete X and Y and Probabilities y = 1 0.1 y = 2 0.3 x = 1 x = 2 find Pr(X = 1,Y = 2). 0.2…

A: From the provided information, Probabilities y = 1 y = 2 x = 1 0.1 0.3 x = 2…

Q: If n=10 and p=0.5, find P(x=8) Give at least 4 decimal places.

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Q: 1. Under Ho, the likelihood function is given by L(Î.) %3D A. True O

A: Let xi; (i=1,2,...,m) be a random sample of size m from a population with probability density…

Q: If the random variable X has the pelf Find a) P(-1 ≤X <14) X 20) b) E(X(2-3X)) f(x)=(X-31/10),…

A: Solution is given below

Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

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Q: Suppose that a random number  is chosen from the interval (0,2). What is the probability that the…

A: Given: The random number is chosen from the interval (0,2). Quadratic equation is 4x2-x+k

Q: a) Calculate the area to the left of z = 2. 25 b) Caleulate the probability P(X >-1,89) c) Calcualte…

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

Q: If the joint probability is given by: f(x,y) = (2x + 2y)/40, for x = 0, 1, 2, 3; y = 0, 1, 2, 3 Find…

A: Given the joint distribution of two random variables X and Y.  Using the joint distribution we have…

Q: t is computed that when a basketball player shoots a free​ throw, the odds in favor of his making it…

A: Given information Odds in Favor = 20:7 Probability that when the player shoots a free throw and…

Q: An insurer has data on losses for four policyholders for 7 years. The loss from the ™ policyholder…

A: Given  r=4,  n=7 ∑i=14∑j=17Xij-X¯i2=33.60 ∑i=14X¯i-X¯2=3.30

Q: I want to know how to solve it.

A: The given equations are,

Q: If X is a continuous random variable with p. d.f. (X f(x) = }6 ,0 <x< 3 12 ,othewise

A: Given pdff(x)=x6+112,0≤x≤30otherwise The probability distribution of Y is calculated as shown below.…

Q: Express in words what the random variable Xm9-1 represents (Hint It is the length of which renewal…

A: given that P{X(subscriptN(t)+1) &gt;= x}&gt;= F(x)but by defnition of F(X) = p(X&lt;=x) ,here…

Q: In the U.S., for fellowship, the Casualty Actuarial Society requires passing a series of nine…

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Q: The three random variables, a, b and c are independent and each uniformly distributed in the…

A: We can find the roots of any quadratic equation ax2+bx+c=0 using the discriminant as follows:…

Q: Show that if t" = (t+t) where t and ť are both most efficient estimators with variance v, then var…

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Q: 1. Determine the requested probabilities. -2 -1 1. f(x) 0.2 0.1 0.4 0.2 0.1 a) P(xs 2) b) P(x > -2)…

A: From the given table Find the probabilities

Q: (b) Let X be a random variable with p.d.f. 2e-2x f(x) =• 0<x<0 find (1) E(x) (2) Var(x) O.W

A: Given the random variable X with p.d.f as fx2e-2x                  0&lt;x&lt;∞0…

Q: -{* S a2-a x = 0, 1, 2, .. Px(x) = { ? otherwise a) Find the constant a b) The base station can…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: Assume b, c are independent random variables with uniform distribution on the interval [-L, L),…

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Q: Consider: f(x, y) = 6x²y,0 < x < 1,0 < y < 1. The probability Pr(-0.5 < x < –1,0 < y < 1) is equal…

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Q: The probability of the joint event {x₁ < X ≤ x₂, Y₁ <Y ≤ y₂} is given as P{x₁ < X < x₂, Y₁ <Y ≤y₂} =…

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Q: If X and Y are independent RVs, each following N (0, 3), what is the probability that the point (X,…

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Q: Let X1, X2, . . . are independent indicator variables with different probabilities of success. That…

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Q: Let X be a positive random variable (i.e. P(X 1/E(X) (b) E(-log(X)) > -log(E(X)) (c) E(log(1/X)) >…

A: Expectation of a Discrete Random Variable: The expectation of a discrete random variable X, denoted…

Q: 2. X and Y are independent and identically distributed Rayleigh variables, each b = 5. What is the…

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Q: Amanda has a von Neumann-Morgenstern utility function given by U VM, where Mis her income. If she…

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Q: 2. Find E(X) and Var(X) if a. P(X = 0) = 0.2, P(X = 1) = 0.3, and P(X = 2) = 0.5. b. X is the number…

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Q: Show that the T(x1,x2,..xn) =x² – is UMVUE of u? with variance - 72

A: Given information: The investigator is specially interested to find the UMVU estimator.

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!