2. For the following discrete variable with probability f(x) X 1 3 4 5 f(x) 0.2 0.15 2c 0.05 0.15 (a) Determine the value of c
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)…
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Q: For the following discrete variable with probability f(x) X 1 2 3 4 f(x) 0.2 0.15 20 0.05 0.15…
A: Given - For the following discrete variable with probability f(x) x 0 1 2 3 4 5 f(x) 0.2 0.15…
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Q: For the following discrete variable with probability f(x) X 1 3 4 f(x) 0.2 0.15 20 0.05 0.15…
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Q: 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…
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A: As per our guidelines, we can solve the first three sub-parts of the first question. Kindly repost…
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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…
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- 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)=___________.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.If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?
- 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.For the continuous probability function f(x ) = kx^2e^-x when 0≤x≤1. Find (a)k (b)mean (c)varianceYou 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?If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?Suppose that the lifetime in years, X, of a type of electrical switch follows the distribution f(x)=12e−x2f(x)=12e−x2for x>0x>0. What type of continuous distribution is this and what is the average lifetime of one of these switches?
- suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.