Q1) Determine the value c so that each of the following functions can ? serve as a probability distribution of the discrete random variable X (x) = c (?) (, ª .)x 4 ),x = 0,1,2,3 x |

Q: Let X₁~N(-1,5), X₂~N(3,2), X3~N(0,1). They are independent rv's. Find the probability distribution…

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Q: a) Find the value of k, b) Form the table of probability distribution of X, c) Find the mean and…

A: here given discrete probability distribution of x p(x) = kx2    for x= 1,2,3,4 here use total…

Q: do №%₂ 6 should Cards r) find the 1) probability PPP) None адачу. are drawn from probability of…

A: Here, X~Bin (n,p) P(X=x)=Cxnpx(1-p)n-x  where, x=0,1,2,3,.....,n. Cxn=n!x!×(n-x)! where,…

Q: Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first…

A: An ordinary (fair) coin is tossed 3 times. outcomes are thus triples of "heads" (h) and "tails" (t)…

Q: Q1) A discrete random variable x has the probability distribution p(X = k) for occurrence of x as…

A: We have given a discrete random variable.x       0  1    2   3  p(x)   k  2k 3k 4kWe have to…

Q: Let P(x) = , x = 0,1, 2,3 be a probability distribution for a discrete random variable X, find: %3D…

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Q: Suppose that P is a probability measure defined on the sample space S. Prove that P(AOB")=1-P(A)–…

A: Solution: 3. It is needed to prove that

Q: Suppose a and b be two possible values of a random variable X with a > b The probability that lies…

A: Given that a and b be two possible values of a random variable X with a > b The probability that…

Q: Find the variance of probability function 1 2 4 P(X) 0,25 0,15 0,10 0,25 0,25 21 - O A) 6,80 O B)…

A: Here, X P(X) X.P(X) X2 X2.P(X) 0 0.25 0 0 0 1 0.15 0.15 1 0.15 2 0.1 0.2 4 0.4 3 0.25…

Q: 5. and Y is The joint probability distribution function of two discrete random variable |x -y| 15…

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Q: The amount of time an air-conditioning technician to repair a unit is in between 1.9 and 5 hours…

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Q: 4. Determine the values of c so that the following functions represent joint probability…

A: f(x,y)=c  ,  for x=-2,0,2  ; y=-2 , 3

Q: If X1, X2, ., Xn is a xrandom sample from a N(µ, o) population, write the distribution of…

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Q: 3. Let us consider two discrete uniform distributions X ~ U({1,2,..., k}) and Y U({0, k}). Compute…

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Q: 24. Let X1, X2, .., X 100 be a random sample of size 100 from a distribution with density S(2) = {6…

A: Given that the pdf of random variable X is f(x)=e-λ*λxx!                ; for x=0,1,2,......0…

Q: 2. A. let the p.m.f of X is: p(x) = ab* x = 0,1,2,... a+b=1 Find the median of X ? B. prove that the…

A: The p.m.f of The median of X needed to be determined and the probability-generating function of (-x)…

Q: The probability distribution function of the discrete random variable X is x -1 0 2 5 P(X=x) 0.10…

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

Q: 6) Probability function of X given as follow; f(x)= 1-(x/2);  0 < x< 2 a. Please draw the graph…

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Q: 6. [Maximum mark: 5] The following table shows the probability distribution of a discrete random…

A: Thank you 😊

Q: Let the random variables X₁, X₂ be independent of each other, well and obey the same geometric…

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Q: Q. 1 Deal two cards from a well-shuffled deck of cards. Let the random variable X be the number of…

A: A well shuffled deck of cards has 52 cards in total, 4 aces and 12 face cards. Let X denote the…

Q: 11.The distribution function of a random variable is 1 fæ =(x – 1)* ,1< x < 3 then the probability…

A: Introduction :-  Let X be a random variable.  Weare given a cumulative distribution function for X.…

Q: vo random variables X-(-1,0) and Y=(2,3) are equiprobable and independent. Determine the

A: Given that there are two random variables. X=(-1, 0) and Y=(2, 3). Both equiprobable. That is,…

Q: TRUE OR FALSE. a.) Let X (X₁, X2,..., Xn)' be a random vector with joint cumulative distribution…

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Q: Let X have a uniform distribution on the interval (1, 6). Find the probability that the sum of 2…

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Q: Let X be a random variable such that X B( 12,8/9).

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Q: 8) Let X be a random variable, and let g,(x) and 92(x) any two functions whose expectations exist,…

A: Let X be a random variable and let g1x and g2x any two functions whose expectations exist    where…

Q: Contracts for two construction jobs are randomly assigned to one of or more of three firms, A, B,…

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

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Q: 3. The following table lists the probability function of the discrete variables (X, Y). Known that…

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Q: 승x, FX=0,2, 4 P(X) =- 0, if X = 1, 3 what is the value of P(x>2)?

A: Given: PX=16X,              x=0,2,4=0,     if x=1,3

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…

Q: ransist aple transistors, then 1) find the probability that a sample has: i-One defective…

A: Since there are multiple questions, all parts from question 1 is answered.

Q: P(-∞ < x≤ a₁₂) = P(a₁ ≤ x ≤ a₂) = P(a₂ ≤ x ≤ a3) = P(a3 ≤ x < ∞) = function p(x) a₁ = = 1 π(1 + x²)…

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Q: A city bus runs every 6 minutes on a certain route. Let X be the waiting time of a passenger…

A: A city bus runs every 6 minutes on a certain route  X  is the waiting time of a passenger arriving…

Q: What is the pmf of X? Calculate the expectation of X.

A: The moment generating function of random variable X is defined as mX(t) = E(etX)

Q: fx, (x) = 0.1 0.95-r

A: The probability distribution of the random variable X1,X2 and X3 is given as- fX1x=5x×0.1x×0.95-x,…

Q: 2. Let X be a random variable with p.m.f., (1+x? 20X = -1,0,1,2,3 0 ,otherwise. f(x) = Find E(3X² +…

A: Given function isf(x)={1+x220,    x=-1,0,1,2,30         ,   otherwise

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!