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

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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: 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: 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!