Let X = (Y,Z) be the fair dice roll with E(Y) = {1,...,6} with PY (y) = 1/6, and Z being an independent fair coin toss with E(Z) = {0,1} and PZ(z) = 1/2.   What is the probability of the event that z + y = 2? What is PZ|Y (1|6)?

Q: (b) Let a discrete random variable X have the following PMF: p(x) = k (=) , for x = 1,2, . ..; 0,…

A: Basic probability

Q: (45) Let X be a random variable with p.d.f. ((k + 4)(x+2) 0<x<2 f(x)=- find (1) k (2) E(x) O.W

A: (45) (1) The random variable X with p.d.f is, fx=k+4x+2      0&lt;x&lt;20…

Q: In a class of 8 students, what is the probability that at least one was born in July?

A: c) Given that there are 12 months in a year. The probability that student born in July is…

Q: Suppose the joint probability distribution of X and Y is given by f(x,y)= parts (a) through (d). (a)…

A: X=3 X=4 X=5 X=6 Total Y=4 7114 8114 9114 10114 34114 Y=5 8114 9114 10114 11114 38114…

Q: 9) You are given the following data regarding the probabilities of two events E and F: P(EUF) = 0.8,…

A: For any two events A and B, union of A and B, is the occurrence of either A or B or both. In other…

Q: do №%₂ 6 should Cards r) find the 1) probability PPP) None адачу. are drawn from probability of…

A: Here, X~Bin (n,p) P(X=x)=Cxnpx(1-p)n-x  where, x=0,1,2,3,.....,n. Cxn=n!x!×(n-x)! where,…

Q: Suppose you are flipping biased coin, which has result of head with probability p.

A: Step 1: For X, the number of tosses until the first head, E(X) = 1/p and Var(X) = (1-p)/p^2 Step 2:…

Q: If X and Y are independent, then what is the probability of the event Y > 4X?

A: Iy is given that X follows U(0,1), then pdf of X is f(x) = 1, 0 &lt; x &lt; 1 And Y follows U(0,2)…

Q: Q.3. Let X be the random Variable with the following probability distribution: X: 9 P(X): 1/6 1/2…

A: Note: According to Bartleby, expert solve only one question and maximum 3 subpart of the first…

Q: Problem 3: The joint probability distribution of the discrete variables X and Y is expressed in the…

A:

Q: Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

A:

Q: (8) X and Y are independent events. P(X)=0.3; P(Y)=0.4. Find (d) P(X or Y) (9) Repeat the previous…

A: " Or" indicates union.

Q: A four-sided die has two faces numbered 0 and two faces numbered 2. Another four-sided die has its…

A: Given that, a four-sided die has two faces numbered 0 and two faces numbered 2. i.e.0,0,2,2. Another…

Q: Suppose that E and F are two events such that Pr[E] = 17/29, Pr[F] = 13/29, and Pr[EN F] = 8/29.…

A: Given, P(E) = 1729P(F) = 1329P(E∩F)=829

Q: (40) Let X be a random variable with p.d.f. (k +4)e¯3x f(x) ={ 01) O.w

A: a)Use the condition of valid pdf to find the value of k…

Q: Let X denote a random variable that takes on any of the values -1, 0, 1 with respective…

A: P(X = −1) = 0.2,P(X = 0) = 0.5,P(X = 1) = 0.3.

Q: (13) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) ={ , find E(e2*) O.W

A: Solution :  Given :  f(x) = 2e-2x    0&lt;x&lt;∞0   o.w     E( e-2x )  = ∫x e-2xf(x) dx…

Q: Determine the following probabilities: P(X > 0.25, Y 0.25, Y 0.25, Y < 4.5) = 1/2 P(Y < 1.5) = 2/3

A:

Q: (5) Let X be a random variable with p.d.f. k 1<x<o 2 f(x) =< , find k. O.w

A: Given: fx=kx2            1&lt;x&lt;∞0                 Otherwise

Q: find P( X' ∩ Y)

A: Here given x and y mutually exclusive

Q: Determine the following probabilities: P (X > 0.25, Y 0.25, Y 0.25, Y 0.25, Y < 4.5) = 5/8 P(Y <…

A:

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

A:

Q: 13. The loss random variable X has a probability generating function 1 P(z) = = 2-z What is E[XA 3]?

A:

Q: The probability of event A, given that event B has occurred, can be found using Ba P(A) P(BIA)…

A: Probability quantifies the chances of an even happening. The probability values always lies in the…

Q: Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)?…

A: PGF of a Random Variable is given by, Gx(t) = Σ tx P(X=x)

Q: 3. The following table lists the probability function of the discrete variables (X, Y). Known that…

A:

Q: When a man observed a sobriety checkpoint conducted by a police department, he saw 660 drivers were…

A: Probability theorem :  P(W)+P(W¯ ) = 1

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: 0.24, P(B) For events A, B and C we have that P(A) 0.26, P(ANB) = 0.05, P(An C) = 0.05, P(BNC) =…

A: P(A) = 0.24 P(B) = 0.26  P(A∩B) = 0.05P(A∩C) = 0.05P(B∩C) = 0.05P(A∩B∩C) = 0.02P(A∪B∪C)' = 0.33P(C)…

Q: . Suppose the probability of selecting a number from the interval [0, 2] is given by f(x) = Cx. (a)…

A: Given f(x)=Cx, 0&lt;x&lt;2,

Q: Let X be a random variable with p.d.f. ((k +4)(x+2) f (x) ={ 0<x<2 , find (1) k (2) E(x) O.W

A: (a) We know, ∫fx dx=1∫02k+4x+2 dx=1∫02kx+2k+4x+8 dx=1kx22+2kx+2x2+8x02=12k+4k+8+16=16k=-23k=-236

Q: Let X be a random variable having p.d.f. fx(x) = cx², -2 < x < 2. For the following parts, your…

A: Given density function: fx=cx2, -2&lt;x&lt;2 c value: ∫-22fxdx=1 from the total probability…

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

A: Given, X be a random variable with p. d. f. f(x)=12kx-2   ; 1&lt;x&lt;∞0           ; O.W. constant k…

Q: (40) Let X be a random variable with p.d.f. (k +4)e-3* f(x) =- 01) O.w

A:

Q: (d) If we define the events A and B by: A = {(X,Y):2(Y – X) > Y + X} Determine P(Ān B).

A: To find the probability of the said event please repost the question with the respective probability…