What is the distribution of X + Y when X and Y are independent random variables with uniform distribution in (0, 1)?
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What is the distribution of X + Y when X and Y are independent random variables with uniform distribution in (0, 1)?
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- A football team makes a team of 6 players, 50% available for selection are women and all players are selected randomly. Let X be a random variable that counts the number of women that are picked to be on the team of six. (i) State what distribution X has, including parameter value(s). (ii) What is the probability of having exactly 2 women on the team? (iii) What is the probability of having strictly more men than women on the team? iv) How many men are expected on the team?Let X be a random variable with a uniform distribution over the interval [-2 , 4]. Determine the standard deviation of X.For the X random variable known to have a Fuzzy Normal Distribution the parameters belonging to the distribution are the triangle with u = (12,17,18) and &2 = (4,5,9) %3D are fuzzy numbers. For this random variable, the fuzzy probability of P [13,16.5] Calculate for a= 0.19
- Please give full details!Suppose that X1,X2,...,X200 is a set of independent and identically distributed Gamma random variables with parameters α = 4,λ = 3. Describe the normal distribution that would correspond to the sum of those 200 random variables if the Central Limit Theorem holds.Assume that X₁, X2,..., Xn are independent and identically distributed random variables with expectation and finite variance o2. What is the approximate distribution of Sn = X₁ + X₂ + + Xn? (State all parameters of the distribution.)
- Suppose a random variable X following χk2. Describe the distribution of X/k when k is large enough.Consider the probability distribution for the number of red balls when 4 balls are selected at random from a box consisting of 5 red balls and 4 purple balls. Let the random variable X represents the number of red balls. a) Find F(0) b) Determine P(X≤3) c) Determine P'(X≤4) d)Determine P'(5) e) What is the value of random variable X if F(x) = 9/14?If n independent random variables have the samegamma distribution with the parameters α and β, find themoment-generating function of their sum and, if possible,identify its distribution.
- Q2) Suppose that X is a continuous random variable with probability distribution £x(x) = ₁ 0≤x≤4 Find the probability distribution of Y = (x - 2)².The number of fish that a person catches per hourat Woods Canyon Lake is a random variable having the Poisson distribution with λ = 1.6. What are the probabil-ities that a person fishing there will catch (a) four fish in 2 hours;(b) at least two fish in 3 hours;(c) at most three fish in 4 hours?