Suppose X is continuous random variable if there exists a nonnegative function f(X) is called random function .a O binomial function .b O probability mass function .c O probability density function.d O

Q: If the probability density function of a continuous random variable X is 0.50x 0<c< 2 0 <x f (2) = {…

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Q: For a random variable which can be defined using the probability density function below, what is the…

A: It is an important part of statistics. It is widely used.

Q: Let X be a random variable have the probability density function 4 e f(x)= x >0 4 otherwise then X…

A: Note:x~exponentialλ                 λ&gt;0x has propability density function given byf(x)=λe-λx…

Q: Let X be a random variable with probability density function, What is Var(X)? f(x) = cx(5-x) for…

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Q: Let 1 1 f(x) = Ix-31, 1≤x≤ 5. 4 Deduce that the function above is a probability density function of…

A: Solution

Q: Suppose that the random variables X and Y have the following joint probability density function.…

A: Given information: The joint probability density function of X and Y is as follows: fx,y=ce-8x-4y…

Q: Suppose X1 and X2 are two independent random variables with the following density function - Cx if…

A: Given density function is, fx=-cx,  -5&lt;x&lt;0       ∫-50f(x)dx=1∫-50(-cx)dx=1-cx22-50=1-c0-252=1…

Q: Let x be a random variable with a probability density function defined by the form f(x) = ke */2, x…

A: We have given that X be a random variable with a probability density function defined by the form…

Q: The probability density function of the random variable X is given by: f(x)=n for 0 < x< 10, and…

A:

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

A:

Q: If X is a random variable with probability density function 32 f (x) = for x = 0, 1, 2, 3, 4 and 5,…

A: Formula : Variance :

Q: Let X be a continuous random variable with the following probability density function: f(x) = {k(6x…

A: Solution

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 continuous random variable with the following probability density function: f(x) ={ 8 %3D…

A: Given:

Q: Consider the probability density function for a random variable X, given by for 0 < x < 5 10 f(x) =…

A:

Q: Suppose that the random variable X has the probability density function c(1- x2) for -1 s x s 1 f(x)…

A: We want to find the probability  P(0&lt;X&lt;1/5)= ?

Q: The probability density function for a continuous random variable X has the form, Find the…

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Q: Let X be a random variable with probability density function S c(8x – a?) if \ 0 8

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Q: If X is the continuous random variable whose probability density function, Find P(-2≤x≤3) for 0≤x≤ 4…

A:

Q: The random variable X has a probability density function given by: k 1<x< 10 f(x) =} Vx- otherwise…

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Q: 3. Suppose that the probability density function of x is f(x) = {°0," (3x?, 0<x < 11 0, elsewhere)…

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Q: Consider the probability density function if x -4 + (x+4)³ Find Pr(X > –1|X < 3). Select one: 18 40…

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Q: Consider the probability density function if x 1. 2x4 Find E(X). Select one: | -IN -|0 O O O O

A: Obtain the expected value of E(X).   The expected value of E(X) is obtained below as follows:   From…

Q: Suppose that the probability density functions of x is 3x2, 0<x < 1) F(xE0, Elsewhere ) a) Determine…

A: Given that,  P.d.f. is f(x)= 3x2, 0&lt;X&lt;1 C.d.f. of X is given by, F(x)= integration|0x f(x)dx

Q: If the random variable Y has the following probability density function f(G) = }5 ,0 <y<5 (0…

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Q: The probability density function of X random variable is given as, f(x)=c(x2 +1), -2<x<2 and f(x)=0,…

A: Given,f(x)=c(x2+1)  ;  -2≤x≤2

Q: Suppose that the random variable X has the probability density function S (1- x) for -1s x s1 f(x)…

A: We have the  random variable X  has the probability density function.

Q: Suppose that the random variable X has the probability density function c(1 – x²) for - 1s x s1 f(x)…

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

A: Given:

Q: Consider the following probability density function 0 < x < 2 (æ) = { +(4 – x) 2<x < 4 %3D |…

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Q: For a continuous random variable x, the probability density function f(x) presents

A: Since ,  For a continuous random variable X , the probability density function f(x) represents…

Q: Suppose that the probability density function of x is f(x) = 0, (3x², 0 (2/3)) b) Determine the…

A:

Q: a) What must c be for the function to be a probability density function? b) Calculate F(1).

A: c can be calculated as:

Q: If the probability density function of the ran lom varinble X is (1- p)-'p if z = 1,2,3, 4,., 00…

A: Given The probability function of random variables.

Q: Let (3x2, 0< < 1 p(x) = otherwise Show that p(x) is a probability density function. Compute its…

A: Given:p(x)=3x2,0≤x≤10otherwise

Q: If the probability density function of a continuous random variable X is 0.50x 0x) = 0.4

A: Given,f(x)=0.5x   ;  0≤x≤20         ;  otherwise

Q: Suppose that the random variable X has the probability density function c(1– x?) for - 1< x <1 f(x)…

A: Answer - The random variable X has  the probability density function                f(X) = c(1-x2)…

Q: If the probability density function of random variable X is given by: f(x) = {o." ( kx? + x, x €…

A: Given ,f(x)=kx2+x  ;  x∈0,10           ;  otherwise

Q: The function 2x 1<x<2 f(x) other wise is a probability density function for a continous random…

A: Answer: ⊙ False

Q: Q1- The probability density function of the random variable X is as follows: X=x 1 1 1 1 P(X=x) 4. 4…

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Q: Find E(X) and Var(X)

A: Since , the probability distribution is given by ,  = 0 ; otherwise Now , we want to find the E(X)…

Q: 3. Suppose that the probability density function of x is [3x?, 0<x < 11 0, elsewhereS f(x) = a)…

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Q: Why is P(X = c) = 0 for any number c in the domain of a probability density function?

A: There are two types of function in probability. One is for Discrete random variable and the other is…

Q: If X is the continuous random variable whose probability density function, Find P≤2 for 0≤x≤ 4 f(x)…

A: In question, Given that X is a random variable having pdf f(x). Then we'll find P(X ≤ 2). The…

Q: A random vartable X with probability density function fo) - 1.5x? for -1 <x<1 has vartance- 240…

A: Since, you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine the probability density function of the random variable X* if x 1 ON|30

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Q: Let X be a continuous random variable with probability density function 1 fx(x) = -1 1/4) is

A: P(X2&gt;1/4)=1/2 (e).

Q: Consider a continuous random variable with the following probability density function: f(x) = 4x', 0…

A: We have given that,  X be a continuous random variable having probability density function is,  f(x)…

Q: Let X be a random variable with probability density function, What is EX? f(x) = x(5-x) for 0≤x≤5 0…

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Q: Suppose that the probability density function of a random variable X is as follows: f(x)= cx,…

A: GIVEN THAT:       f (x)= cx for0&lt;x&lt;4; 0, 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!