The probability density function fX (x) of the random variable X fX(x) =(  4x3            0 < x ≤ 1            (  0            otherwise       given in the form.  P(X ≤2/3|X > 1/3) Find the probability of the event

Q: f(x) = 6 () 0.3* for x = 0,1,2 %3D serves as a probability distribution function of the random…

A: # Given: probability distribution of random variable x is f(x)=theta*(2 C x)*(0.3)^x  X:0,1,2  Then…

Q: The probability distribution of a discrete random variable X is given below. Value x of X P(X=x) -1…

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Q: The distribution function ‘F’ is given by F(x) = 0, x < 0 ½, 0 ≤ x <1 3/5, 1 ≤ x < 2 4/5, 2 ≤ x < 3…

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Q: Let X and Y be independent exponential random variables, both with mean β = 2. Find (and show your…

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Q: Q6. (a) The continuous random variable X has a probability density function given by 2 1 C 2 1< x<2…

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Q: 3. probability distribution in equation form X 8/1 72 f(x)= ; x = 1, 2, 3 (a)P(X ≤ 1) = (b)P(X> 1) =…

A: X 1 2 3 f(x)=P(X) 4/7 2/7 1/7

Q: Let X be a random variable with probability density function given by x -1 0 1 f(x) a b 0.25

A: From the given information, x -1 0 1 f(x) a b 0.25 From the probability condition,…

Q: Let X be a random variable with p.d.f f(x) = c+ 1.2x2,0<x< 1. Find a constant c if E(X) = ! 0.6 0.4…

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Q: Consider the probability distribution function (PDF) f(x) = Ax sin x, for 0 <xs N (a) Consider…

A: a) Given that  The value of A is calculated below:                ∫0πf(x)dx=1…

Q: A coin is tossed n times, and heads turns up with probability pon each toss. Assuming the usual…

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Q: f (x) x=0,1,2,3 Define the following probability function the value of the expectaion E(X-1) is 1 2…

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Q: The probability density of the random variable X is given by: (x+1) for 2<x<4 f(x)=. otherwise Use…

A: Given: The probability density function of the random variable X is given as: fx=18x+1 for…

Q: The probability density function of a mixed random variable X is as follows: Af(x) 0.108(41) 0.20…

A: Given the probability density function of a mixed random variable X as

Q: Let X be the total medical expenses (in 1000s of dollars) incurred by a particular individual during…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: Let X and Y be two independent continuous random variables whose joint probability distribution is…

A: Given joint probability distribution is: fx,y=100e-10xe-10y0&lt;x&lt;∞, 0&lt;y&lt;∞0Otherwise a). As…

Q: Consider the probability distribution function (PDF) f(x) = Ax sin x, for 0 <x< N (a) Consider…

A: (a) Given that f(x)=Axsin(x) is a probability distribution function. So, ∫-∞∞f(x)dx=1 Now,…

Q: The probability distribution function of a random variable X is P(X =x)= k for x 0,1,2,3,4 where k…

A: (a) We know that  ∑X=04P[X=x] = 1, hence    k=116  answer P(0&lt;X&lt;4) = P[X=1] + P[X=2] + P[X=3]…

Q: A probability distribution is given. -1 POO 0.2 0.3 0.5 Find caf. Xs-1 0.2 -12 Xs-1 0.2 -12 x<-1 0.2…

A: The cumulative distribution function is on the real number line and it is a non decreasing function…

Q: 48) Let X be a random variable with p.d.f. 1 -8x 0<x<00 k f(x)= , find k. O.w

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Q: (b) A continuous p.d.f for a random variable X with function, P(x) = SX for 01|x< 4).

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Q: Suppose that X is a continuous random variable whose probability density function is given by (4x –…

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Q: a) A continuous random variable can be represented as X e R. (True/False).

A: As per guidelines we answer question only when multiple different question are given. Please post…

Q: ndom variable X has cumulative distribution function F(x)given by 0. F(x) =- 6. +2x-2 , 2sxS3 1 x2 3

A: a. P(1&lt;X&lt;2.2) = F(2.2-) - F(1) = F(2.2) - F(1)  = -2.223+2*2.2-2 - 126 = 0.62

Q: The probability distribution of a discrete random variable X is given below. Value x of X P (X=x) 3…

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Q: f (x) = 0, %3D pendently selected, find the E

A: The number of sample is n=4. a. The probability of impurity weights exceeds 0.5 is,…

Q: -2 kx 1<x<0

A: The probability density function given is, fx=12kx-2 , 1&lt;x&lt;∞0 , o.w Here X is the random…

Q: The probability distribution of a discrete random variable X is given below. Value x of X P(X=x) -3…

A: HERE GIVEN PROBABILITY FUNCTION SO HERE CUMULATIVE PROBABILITY = F(a) = P  (X&lt;a)

Q: A random variable X has the probability density function (pdf) shown in he figure below. fx (2)

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: 4 The continuous random variable X has cumulative distribution function: x 3 Find: a P(X> 2.4) b the…

A: I solved exactly 3 subpart of given question... because of bartleby policy. If you want more please…

Q: Which of the following represents the two properties a continuous probability distribution must…

A: Given, The properties of distribution function and probability density function.

Q: A random variable X has the probability density function (pdf) shown in he figure below. -2 1 4 Let…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: f(x), a continuous probability function, is equal to 1/12, and the function is restricted to 0<x<12.…

A: Given that  f(x) = 1/12 for 0 &lt; x &lt;12

Q: 3 The probability density function of a continuous random variable is given by cx, 0<x<1 f(x) = {,…

A: Step 1: Since you have posted a question with multiple sub parts we will solve the first three parts…

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Q: Find the value of a

A: A function  f: ℝ→ 0,1 is said to be a probability density function if i.  f(x)≥0 and ii. ∫-∞∞f(x)…

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!