2. For the following discrete variable with probability f(x) X 1 2 3 4 5 f(x) 0.2 0.15 2c 0.05 0.15 P(X<3)
Q: 2. For the following discrete variable with probability f(x) 1 3 4 f(x) 0.2 0.15 2c 0.05 0.15 (b)…
A: Given:
Q: Suppose f(x) is pdf and is the mean of the random variable, then |(x – 4° f (x) dx = / x²f (x) dx –…
A:
Q: 3. Given that the continuous random variable X has distribution function Fl2) as F(x) =0 when 2<1…
A: The graph is given below: From The graph it is concluded that when x approaches 1 from both the…
Q: (d) E(Y) = (e) For 0 < x < 1 marginal probability distribution of X is 16 -for 0 < x < 1;÷for 1 < x…
A:
Q: 4 The random variable X has p.d.f. 1 f(x) = for -2 <x<4 = 0 otherwise. (i) Sketch the graph of f(x).…
A:
Q: 3. Suppose that the joint denstiy function of X and Y random variables is (2x+3y S(x, y) = { 23 1<x<…
A:
Q: 4 The continuous random variable X has p.d.f. f(x) where for -3 2.5)
A:
Q: 16. Show that for the chi-square distribution 1 2 2. 1 f (x³) d (x³) = X (x) e 2n/2 r n/2 H (about…
A:
Q: 13. If X has the distribution function for x<-1 1 for -1 sx<1 F(x) for 1Sx<3 for 3<x<5 1 for x25…
A:
Q: 1<x < 3 | f(x) = {C(x - 1)(3 – x) diğer
A:
Q: 10- Referring to table beside, When Epxy (x, y) = 0.01, then: %3D a- X= 2.5 Table: Discrete joint…
A:
Q: Q4: For the continuous probability function f(x) = 2kx²e-* when x > 0. Find a. Value of k %3D b. b.…
A: The definition of Gamma Function is given by, Γn = ∫0∞xn-1 e-x dx For any integer n, Γn = (n-1)!…
Q: What is the probability that x is between 3 and 6, given the function below? f(x) = (1/10) e-x/10…
A: Given ,fx=110e-x/10dx : x≥0P3≤x≤6=?
Q: 5. If X and Y have the joint probability distribution f(x, y)=1/4, for x=-1and y=-1,x=-1 and y=1,x=1…
A: Given: fx,y=14=0.25 The joint probability function is shown below X -1 1 Y -1 0.25…
Q: A random variable, x, has p.d.f. f (x) given by f (x) = 1 а. always equals 1 b. 0 < x< 1 C. Not…
A: We know that, If a random variable x having probability density function f(x) by the property of…
Q: Consider the three functions I. f(x)= {1-x if 0 < x < 2 {0 otherwise II. f(x)= {1+x if 0 < x < 2 {0…
A: f(x) can be probability distribution function if integration|xf(x)dx = 1 It means the total…
Q: (b) Suppose that the random variables X and Y have the joint p.d. f. f(x, y) = {kx(x – y),0 < x <…
A: Given : f (x , y) = kx x - y , 0<x<2 , -x<y<x0 , elsewhere (i) To…
Q: What is the expected value of the function g (X, Y) = (XY)²
A:
Q: EX. I The joint probability muss function of two discrete random variables X and Y is given by:…
A:
Q: 2 (25') The continuous type random variable X has pdf for 0 1].
A: We know that, Total probability= 1 So ∫04cxdx = 1 c(x2/2)04 = 1 c (16/2 -0)= 1 c=1/8
Q: 1. Suppose that X and Y have the following joint probability distribution Y 1 2 3 1 0.05 0.05 0.1…
A: As per our guidelines, we can solve the first three sub-parts of the first question. Kindly repost…
Q: 7) The probability density function f(x) of a continuous random variable is given by cx+3 for-3<x<-2…
A: Given: The probability density function of random variable X is given as:…
Q: Suppose X is a continuous random variable with p.d.f. fX(x) = kx2(1 − x) if 0 < x < 1. (b) Find the…
A:
Q: Suppose that f(x) = e* for x > 0. Determine the following probabilities: Round your answers to 4…
A:
Q: Determine whether the following is a valid distribution function: (1- e-x/2 . x 2 0 F (X) =
A:
Q: f(x) for a continuous probability function is 1/18 , and the function is restricted to 2 ≤ x ≤ 20.…
A:
Q: Verify that the following is a distribution function: X a
A:
Q: I1. If X has the distribution function for x<1 for 1sx<4 F(x) for 4 sx <6 for 6sx<10 for x 10 find…
A:
Q: Which of the following represents the two properties a continuous probability distribution must…
A: Given, The properties of distribution function and probability density function.
Q: The following is a probability distribution function for X, with range 0, 1, 2, P(X = 0) = 0.3 P(X =…
A: The probability distribution is given by X 0 1 2 3 P(x) 0.3 0.3 0.2 0.2
Q: | X*-PCx) Number of Boxes I probability x- P) of breads x PCx) 0.20 0.25 10 15 0.30 20 0.15 0.10…
A:
Q: 1. Suppose that the lifetime in years, X, of a type of electrical switch follows the distribution f…
A: Given equation is the pdf of an exponential distribution with mean 2 X is an exponential…
Q: 2. For the following discrete variable with probability f(x) X 1 2 4 f(x) 0.2 0.15 2c 0.05 0.15 By…
A: Given:
Q: Why the probability P(X=x)=0, for a continuous variable,?
A: Given info: The probability P(X=x)=0, for a continuous variable
Q: Suppose that f(x) = e* for x > 0. Determine the following probabilities: Round your answers to 4…
A: Givenf(x)=e-x ; x>0
Q: We know the marginal probability Pr(X=D0) = 0.25 (from the table) and the following conditional…
A:
Q: a f(x) = x for -1sxs1, and O for any other value of x %3D then, the percentage probability P-sxs is
A: Introduction :Here we have ,
Q: 5.6 Given the probability density f(x) = for 1+x2 00<x < 0, find k.
A: Given: f(x)=k1+x2 for-∞<x∞
Q: 1. If X has the distribution function 0 for x1) e. P(-0.4 <X< 4) f. P(X = 5) 114
A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…
Q: Consider the following normal distribution: 1 f(x) = exp[-1/2(x– µ)²lơ²] Show that f(x) is a…
A: Given:
Q: Denote by { 1* 0 <x<1 0.5 2< x <c . elsewhere f(x) = Find the value of c, such that f(x) is the…
A: Solution: From the given information,
Q: The following six graphs oorrespond to three probability density functions and their cu- mulative…
A: GivenSix graphs which represent either a probability distribution function or cumulative…
Q: Which of the following is a required condition for a discrete probability function?
A: Given: Which of the following is a required condition for a discrete probability function? Σf(x)…
Q: f(x), a continuous probability function, is equal to 1/12, and the function is restricted to 0 ≤ x ≤…
A:
Q: 13. If X has the distribution function for x<-1 1 for -1 sx< 1 Fx) for 1sx<3 for 3sx<5 for xz5 find…
A:
Q: 5. If X and Y have the joint probability distribution f(x, y)=1/4, for x=-1and y=-1,x=-1 and y=1,x=1…
A: Given: fx,y=14=0.25 The joint probability function is shown below X -1 1 Y -1 0.25…
Q: 2. z = -0.00 z = -1.40 Z = -0.80 10. Find the z-score corresponding to a score of X = 45 for each of…
A: Given ,score(X)=45and we know that Z-score=X-μσ
Q: Suppose that X and Y have following joint probability distribution: F(x,y) X 2 1 0.10 y 3 0.20 5…
A: Given that Joint probability function. F(x,y) X 2 4 Y 1 0.10 0.15 3 0.20 0.30 5 0.10…
Q: 5.2.1 The conditional probability distribution of Y given X = x is fy.0) = xe-y for y> 0, and the…
A: We have to answer question based on exponential distribution and uniform distribution.
Q: What value for k allows the following f(y) to qualify as a continuous probability function? f(y) 2k…
A:
Step by step
Solved in 3 steps with 3 images
- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?Suppose that the random variable X is continuous and takes its values uniformly over the interval from 0 to 2. What is P{X = 1.5 or X = 0.4}?
- Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the secondhaving μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated,with ρ = −0.8. Denote the expected return and its standard deviation as functions of π byμ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as πvaries from 0 to 1. Plot this curve in R.Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.You consider investing £800 in stocks of the company X for a certain period. There is a possibility for X to merge with Y, in which case you expect your investment to appreciate £300, otherwise you expect it to depreciate £200. Also, rather than investing, you can choose to keep your £800. By using a utility function U(x)=x−−√, and by defining pthe probability that X merges with Y, what is the condition that p must satisfy for your investment to be worthwhile (rounded to two decimal places)?
- Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?When a certain glaze is applied to a ceramic surface, the probability is 5% that there will be discoloration, 20% that there will be a crack, and 23% that there will be either discoloration or a crack, or both. Let X = 1 if there is discoloration, and let X = 0 otherwise. Let Y = 1 if there is a crack, and let Y = 0 otherwise. Let Z = 1 if there is either discoloration or a crack, or both, and let Z = 0 otherwise. a) Let pX denote the success probability for X. Find pX. b) Let pY denote the success probability for Y. Find pY. c) Let pZ denote the success probability for Z. Find pZ. d) Is it possible for both X and Y to equal 1? e) Does pZ = pX + pY? f) Does Z = X + Y? Explain.Suppose X is a continuous random variable with p.d.f. fX(x) = kx2(1 − x) if 0 < x < 1. (b) Find the c.d.f FX(x) explicitly.
- Let Y be a discrete random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2Let Xi be arandom sample from U(0,1)prove that Xn’ convarges in probability to 0.50If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.
