QUESTION 1 The probability distribution of random variable X is a) b) c) Show that k = 6. Find P(X < 3). P(X = x) = k + X 2k 0 ) } x = 0 x = 1,2,3,4 elsewhere Compute the expected value of X. Hence, calculate E (2x − 3).

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A: We know that  The sum of the probability is equal to 1. ∑P(X=x)=1

Q: Find (a) The constant K (b) P(X> 1) (c) P(|x|<3)

A: To determine the value of K we will use the fact that the integration of pdf f(x) over whole range…

Q: (b) Let a discrete random variable X have the following PMF: p(x) = k (=) , for x = 1,2, . ..; 0,…

A: Basic probability

Q: The discrete random variable X has the probability distribution 2 4 P(X=x) k 2k 3k 4k 3.

A:

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Q: Assume that the cumulative distribution function of the random variable X is (image): Determine the…

A: i) Since, -2&lt;1.8&lt;2 , so F(1.8) follows 0.25x+0.5 P(X &lt; 1.8)=F(1.8)=0.25(1.8)+0.5=0.95

Q: If X and Y are independent, then what is the probability of the event Y > 4X?

A: Iy is given that X follows U(0,1), then pdf of X is f(x) = 1, 0 &lt; x &lt; 1 And Y follows U(0,2)…

Q: 5. A random variable X= {0, 1, 2, 3, ...} has cumulative distribution function F(x) = P(X ≤ x) = 1 -…

A: Explained Below:Explanation:  Please let me know if you have any queries, so that i could help.

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A: Dear student, According to Bartleby guidelines we can answer only first 3 subparts at once. If you…

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A: As per given by the question,  The mean value is given 3. From Poisson distribution, PX=x=λxe-λx!…

Q: If ‘X’ is a continuous random variable, then the expected value is given by ?

A: For a continuous random variable X it can take values over a continuous range. So while computing…

Q: The probability distribution of random variable X is a) b) c) d) Show that k = 6. Find P(X <3). P(X=…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Q: let X be a random variable and X is normally distributed

A: Given information:  μ=35 and σ=4

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A: Find  Var(3X+2)=? 5E(2X-1)=? E(2X+1)2=?

Q: The discrete random variable X has probability function f(x) given by f(x) = k (lxl + 1)²,x = -1,0,1…

A: It is highly useful in statistics . It is an application of discrete probability distribution .

Q: Let X denote a random variable that takes on any of the values -1, 0, 1 with respective…

A: P(X = −1) = 0.2,P(X = 0) = 0.5,P(X = 1) = 0.3.

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A: We have given that  The random variables X and Y have the joint pdf given by fXY(x, y) = e-x.…

Q: Q6) Let X be a normal random variable with mean equal to 40 and standard deviation 12. Find the…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

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A: Given:   x p(x) -1 0.1 0 0.5 2 0.3 5 0.1 total 1

Q: (2) Let X be a random variable with p.d.f. 1<x<10 f(x) = then o.w 3 (a) k=2 (b) k=8 (c) k = (d) k=3…

A: Solution: 2. From the given information, the probability density function of X is

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A: Givenmean(μ)=3.6variance(σ2)=2.52

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Q: The random variable X has CDF Fx(x) x 2) d) Determine E(X) e) Determine Var (X)

A: Given, the cdf of random variable  X: F(x) = 0          x&lt; -30.4           -3≤x&lt;5     0.8…

Q: 1) Let the probability function of a discrete random variable X be 100) = {(²+²) (0.5) (05) 1-²,…

A: Solution

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A: Given information-

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Q: Find the value of p and work out P(2< X <5).

A:

Q: Q2 (30P) a) Probability function of X discrete random variable: P(x) = { x = 1,2, 3, . .,10 in other…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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A: Solution :  The PDF of random variable is given as, P (x) = cx                      x=1,2,3,...,10…

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Q: Q2 Suppose Y is a discrete random variable such that P(Y= y) = K(1-a)-1,0 < a <1 for y = 1,2,... co.…

A: P(Y=y)=k(1-a)y-1 ; y=1,2,...