Show that if the exponentially decreasing function if x < 0 if x > 0 f(x) = LAe is a probability density function, then A = c.

Q: Consider the following exponential probability density function. f(x) =  1 3e−x/3     for x ≥ 0

A: Solution: The exponential probability density function is f(x)=13e-x3         For x ≥0       0…

Q: Exercise 3.3 Suppose that the probability density function of X is 0 2/3). 0,

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Q: Find the cumulative density function for the given probability density function. k(x) = 1.9 e -1.9X,…

A: Given: k(x)=1.9e-1.9x, for 0≤x≤∞ Cumulative density function will be Kx=∫0xk(t)dt

Q: Suppose that a density function is given by the formula if 0 < x < 10 2 200 f(x) = 2 2 10 x if 10 <…

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Q: Suppose that the joint probability density function of X and Y is fxy(x,y) = 300.125(x² – y²) e-7*,…

A:

Q: e) What is the cumulative density function of X?

A: Solution-: Given: a=5, b=50 Let, X- be the waiting time for the light to turn green in seconds…

Q: The random variable Y has probability density function fv) = k(y+ y³), 0 < y< 2 and zero otherwise,…

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

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: The function f is a probability density function of a random variable x in the interval a,b. fx≥0…

Q: Suppose X~Uniform (0,1), and Y = -ln (1-x). (a). Find the probability density function of Y

A: Given that X follows Uniform distribution with (0, 1). Y=-ln1-X a) Consider, the cumulative…

Q: 4) Suppose X follows Exponential(2), and Y follows Exponential(4). X,Y are independent. (If Z…

A: The answer to the above question is as follows : X~exp(2)f(x)=2e-2x…

Q: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0&lt;x&lt;3,0&lt;y&lt;3

Q: Let f(x) = 0, C:C x² +1¹ 0, if x ≤ 0 if 0<x<√e-1. if x ≥ √e-1 For what value of c is f(x) a…

A:

Q: 4) Suppose the probability density function of the magnitude X of a dynamic load on a bridge (in…

A: The sum of probabilities of all the outcomes is always equal to 1. Therefore, the area under the…

Q: If the probability density function of X is : f(x) = e-x (1+e*)2 en what is the probability density…

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

Q: Find a value for constant A such that x<-1 fx (x) ={ A(1- x*)cos -1<x<1 1< x is a yalid probability…

A:

Q: Let X and Y has joint probability density function AX, Y) = 0<x<2, 0<y<2. 16 Find E( X Y ).

A: Solution: From the given information, the joint probability density function of X and Y is

Q: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…

A:

Q: Let X and Y has joint probability density function AX, Y) = *7 ,0<x<2, 0 <y<2. x y Find E( X + Y)

A: Given a joint probability density function of X and Y , we need to find E( X+Y)

Q: If f(x) = kx, determine the value of k that makes f(x) a probability density function on 0<xs4.

A: Given,           fx=kx2To find : Determine tha value of k that makes fx a probability density…

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: What should be the value of k for f(x) to be able to be a probability density function? f(x)=(2kx)/6…

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Q: If the joint probability density function of X and Y is f(x, y) = e**), 0 < x, 0<y. Are X and Y…

A: Given the joint probability density function of X and Y is fx,y=e-x+y,    x≥0, y≥0

Q: Find a value of k that will make f a probability density functionon the indicated interval.ƒ(x) =…

A: From the definition: The function f is a probability density function of a random variable x in the…

Q: A certain radioactive mass emits alpha particles from time to time. The time betwee emissions, in…

A: Solution

Q: Give the two conditions that a probability density function for [a, b] must satisfy.

A: The probability density function f(x) lies in close interval a to b.

Q: et the density function of a random variable Xt fx(x) = Ox®-1, 0sxs1 0<x<1 ompute the sufficient…

A: The pdf of random variable X is given: fX(x) = θ xθ-1,   0≤x≤1

Q: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…

A: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…

Q: Is the probability density function a valid PDF? * if x 1 F(x) = x2 +=x3/2 %3D ON/30

A: the probability density function i.e., pdf of a random variable X is denoted by f(x) and the…

Q: Let X and Y have the following joint probability density function(pdf): if 0 < x < 1, 1<y<2 f(1, y)…

A: Consider the following pdf- f(x,y)=c.x2y,0&lt;x&lt;1, 1&lt;y&lt;20,otherwise EX|Y=∫01x f(x,y)dxf(y)

Q: A continuous variable Y has a probability density function given by p(y)=Ay^3 for 0≤y≤3 What is…

A: Answer -A continuous variable Y has a probability density function given by p(y)=Ay^3 for 0≤y≤3…

Q: The probability density function of Y = 5X + 3 is:

A: To obtain the probability density function of Y=5X+3, we will use the transformation method.

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Definition used-      The function f(x) is a probability density function, if-     i)  f(x)≥0 for…

Q: 1. Suppose that for a certain life the probability density function is fx (x) = 1+x ,x >0 Find (i)…

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Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Consider the function: fx=kx12, x∈1, 4   and, for all other values of x, fx=0.   Thus, fx=0,x∈-∞,…

Q: Let X be a random variable with probability density function fx(x) given by fx(x)= 0. (2e-2 for x20…

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Q: Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.

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Q: Verify that f(x) is a density function and find also the mean of X.

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Q: If you know that the following function is joint probability density functio f(x,y) = {8xy* {8xy* 0…

A: Given that the density function is, f(x,y)=8xy4, 0≤x≤y≤t The value of t is obtained by using the…

Q: In a psychology experiment, the time t, in seconds, that it takes a rat to learn its way through a…

A: Given density function of time t in second for a rat for its way through maze  f(t)=0.04 e-0.04t

Q: Let X be a random variable with probability density function a+ bx², 0<x<1 f(x) = | 0, otherwise If…

A: We have given that, Let X be a random variable with probability density function…

Q: Suppose that the random variable X has cumulative mass function given by if x 2. What is the…

A: We use the realtion of cdf and pdf to solve the qstn.

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Given: ƒ(x) = kx3; [2, 4] A probability density function equals 1 for sum of all range of values.

Q: Suppose you have two independent random variables X ~ Exponential(A1) and Y Exponential(A2), A1 > 0,…

A: X~Expλ1Y~Expλ2 Here,  λ1&gt;0 and λ2&gt;0 It is given that X and Y are independent exponential…

Q: Q3 If the joint probability density function of X and Y is given by 0 < x < ∞, 0 < y< o∞ f(x, y) =…

A: Ans . Here for calculation of E [ X/Y=y ]  ,  we first calculate marginal distribution of  Y  then…

Q: If X has the probability density function given by (Ke-3x; x > 0 fx(x) = 0; e.w. What is the value…

A: Total probability is always 1.So,…

Q: In a psychology experiment, the time t, in seconds, that it takes a rat to learn its way through a…

A: Let T denotes the time (in seconds) that it takes a rat to learn its way through a maze.

Q: Determine the value of e that makes the function f (x, y) = c(x + y) a joint probability density…

A:

Q: Suppose that a random variable Y has a probability density function given by Sky³e% ,y>0. f(y) = ,0.…

A: Gamma Distribution: A continuous random variable X is said to follow Gamma distribution with…