determine which are probability density functions and justify your answer. 1. ƒ(x) = 1/18  x over [4, 8]  2. f(x)= (2 - x)/2 over [0, 2].

Q: Q3: Choose the correct answer Let X-F (4,8), then 3. The probability density function of X is

A: Formula: Let X follows F(c, d) The density for X is, fx=cxcddcx+dc+dxBc2,d2 Here, c=4 and d=8

Q: The following function is a probability density function ,the value of k is * f(2) = { * otherwise)…

A:

Q: (Mandatory Suppose T has the probability density function fr(t) 2te-, for %3D year-old component…

A: Given the probability density function, fTt=2te-t2  for   t>0

Q: 28. Given that f is a probability density function, 0 < *< 2 where f (x)= {_& 0, elsewhere. the…

A:

Q: 3. Suppose that the probability density function of X is [3x?, lo, 0 < x< 1 f(x) = otherwise…

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Q: Suppose that X takes values between 0 and 1 and has probability density function x2 (2x +). If Y…

A:

Q: If X has probability density function f(x) = x/12 on [1,5], find P(1< x < 2).

A:

Q: Q3 a) f the probability density function (cVx,0< x < 1 f(X)= 0, else where Find the value of c?

A: Given, the probability density function of X- fx=cx, 0&lt;x&lt;10 , elsewhere It is known from the…

Q: e 22 ,x > 0 f (x; λ) 1 otherwise

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Q: 4 Consider the following two functions, each having an unknown parameter c. S(r²+4x +7) -5 <x< 5…

A: It is been asked to verify whether the given two functions are probability density functions and…

Q: B. Consider the probability density function f (x) = kxe³* 13x<2 = 0 otherwise Find the following:…

A:

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: 26, Consider the following exponential probability density function. 1 f(x): 8 for x 20 %3D Find P(x…

A:

Q: The exponential probability density function is f(y, 2)= he- for y, 120 Show that the exponential…

A:

Q: Determine the value of c for which the function below will be a probability density functi So(8x' -…

A: Here given thatf(x)=c8x3-x4   ; 0≤x≤80                    ; other

Q: Q/34 Let c cosx f(x) = >x>0 otherwise be probability density function of X a)Find the value of c…

A:

Q: et it be the probability density function. [ f(x2= n-x 2(1-2). ax Let it be Y = e x=0,1,2, So E(Y)…

A: Solution

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: 3. Consider the function f (x) = B - x/4 for 1 s x s 2 and f (x) = 0 otherwise. Determine the value…

A: Explanation of the answer is as follows

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: 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: For the probability density function f(x) = 3x^2 on [0,1], find: V(X)

A: The probability density function is We know that

Q: Q6. Consider the probability density function fex) = {C A if x>1 Inx %3D X2 otherwise . Ca) Find C.…

A: Given function f(x)=clnxx2if x≥100therwise find c find Px≥3

Q: et f(x) = k(9x − x2) if 0 ≤ x ≤ 9 and f(x) = 0 if x 9. (a) For what value of k is f a…

A: a) The total probability is always 1.So,…

Q: Suppose that X takes values between 0 and 1 and has probability density function x2 (2x +). If Y…

A: The arithmetic mean of squares of deviations taken from the arithmetic mean is called as…

Q: Let f(x)=k(4x -x²) if 03. (a) For what value of k is f(x) a probability density function? (b) For…

A: Given that  Probability density functions of X  f(x)=k(4x-x2)  , 0&lt;x&lt;3 f(x)=0     , x&lt;0 ,…

Q: (4x³ : - Suppose X has probability density function Jx(x)={ 0<x<1. : otherwise

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Q: 3. Find the value of k so that f(x) for 1 < x < 2 is a probability density function. (x + 1)?

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Q: Q.2 Consider the following pdf -x + c; -b <x< 0, fx (x) = x + c; 0 <x< b - (i) Verify that it is a…

A:

Q: Consider the probability density function f ( x ) = kxe^3x        1≤x≤2 = 0…

A: Given information: It was stated that the pdf of x is given as, f(x)=k x e3x ; 1≤x≤20          ; O.w…

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: Consider the following function ke-0.1477(x+8.9)² ,-∞ –10), work with four decimal places or more c)…

A: Given Information: fx=ke-0.1477x+8.92   , -∞≤x≤∞ a) find the value of k. By axioms of probability we…

Q: the following probability density function: f(x) = {k(6x + 2x³) 0 Find the value of k. 0≤x≤B…

A: Solution

Q: What value of c makes the function 0< <1 f(2) = 3e a probability density function? Recall e < 3.…

A:

Q: 4. By the end of 2021, the percentage, X, of the population (expressed in decimals) that will be…

A: Given: The probability density function,         f(x)=kx , 0&lt;x&lt;1 0      , elsewhere

Q: For the one that is a probability density function, find the probability that is between 0 and 0.2.

A: ∫ -∞∞f(x)=1⇒∫ -∞0f(x) + ∫0∞f(x)⇒∫ -∞00 + ∫0∞8e-8x⇒8e-8x-80∞⇒-e-∞-e0⇒-e∞≠1 this is not a pdf

Q: For what value of c is the function if x > 1 f(x): (x) = {C/x9 otherwise a probability density…

A:

Q: Let X and Y have the joint probability density function given by (1. Osxs2, 0sysl, 2y Sx 10. Ow.…

A:

Q: Martian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after…

A: g)   From the given information, the probability density function for X is,

Q: Suppose that the unknown X is ≥ 2  and has the probability density function fX(x)=Ce^−x,x ≥ 2.What…

A:

Q: Letx and be a random variables with probability density function f(xy) = k 0Sxsys1 1- Find the…

A:

Q: Decide whether the function f(x) =7x -5 is a probability density function on [- 1, 1]. If not, tell…

A: Topic:-  probability

Q: 4 Consider the following two functions, each having an unknown parameter c. Sc(a2 + 4x + 7) -5<x < 5…

A: Given, The following two functions:                                                  f(x) = c(x2 +…

Q: Suppose X has probability density function fx (x) = e² for x >0 and fx (x)= 0 otherwise . P(2< X <…

A: The given probability density function is: fXx=35e-35xx&gt;00Otherwise For P2&lt;X&lt;7:…

Q: suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then…

A: In question, Given X has an exponential distribution with probability density function f(x) =2e^-2x,…

Q: Show that the following are the probability density functions: fi(x) = e-*I(0,00)(x) f2(x) =…

A: To prove that f(x) is a pdf, we must show that f(x) &gt;= 0 for all x and, using I[a, b] for the…

Q: [Q1] If the probability density function is f(x) as follows, find: (a) k that makes f (x) a valid…

A: From the given information, Consider, fx={ kx41-x,  0&lt;x&lt;1      ={0,  else Thus,