(d) Calculate the conditional probability P(Y> x =). (e) Calculate the probability P(Y > ¹). (f) Evaluate E(X|Y = y) for any fixed y with 0 ≤ y ≤1.

Q: The probability function of a v.a.d X is -2 -1 1 2 fx (x) 1/8 2/8 2/8 2/8 1/8 P(X -2) = P(-1< X< 1)…

A: We have given that,  X be the random variable having above probability mass function fx(x) .  Then,…

Q: A particle moves along the line in a random walk. That is, the particle starts at the origin…

A: It is given that  PXi=1=0.6, PXi=-1=0.4,

Q: Property 4. If the distribution function of a r.v. X is symmetrical about zero, i.e., if 1– F(x) =…

A:

Q: Let X be uniformly distributed over (a, ß). Find (a) E[X] and (b) Var(X).

A: Given that,X is uniformly distributed over  i.e.

Q: Let z(x) ~N(0,1) Prop (x > -0.56) = Prop (x ≤ -2.17) = Prop (-1.56 ≤ x ≤ 0.72) =

A:

Q: Determine the cumulative distribution function F(x).  Determine the cumulative distribution…

A: Given data is  f(x,y) x 2 4 Total y 1 0.10 0.15 0.25 3 0.20 0.30 0.50 5 0.10 0.15 0.25…

Q: Compute the conditional expectation E(Y|X = 0.4). Are X and Y independent? Explain.

A:

Q: (d) Find the probability P(Y = 1|X=2) = %3D (e) Find the probability P(X = 2|Y =0) = %3D %3D (f)…

A: Given Joint PDF : The sum of all probabilities should be 1 a + 0.3 + 0.4 + 0.2 = 1 a = 1 - 0.9 =…

Q: Let r1 and r2 denote the annual returns of stocks 1 and 2. Assume that (r1, r2) ~ BVN((0.08, 0.05?),…

A: Given  r1, r2~BVN0.08, 0.052, 0.05, 0.152, -0.5

Q: Let F(x) is distribution function then P(a <x sb)=F(b) – F(a) صواب

A: For a continuous random variable XX, once we know its cdf FX(x)FX(x), we can find the probability…

Q: 19 a) Find the probability that X > 0.5 0.4753 b) Find the probability that 0.3 < X < 0.63 0.3423 c)…

A: a) The probability that X &gt; 0.5 is 0.4753. b) The probability that 0.3 &lt; X &lt; 0.63 is…

Q: Let X have a distribution N(2,4). Calculate P(|x| =<1.2) and P(|x| =<11.6) and determine such x for…

A: Given: Let X have a distribution N(2,4) =&gt; μ = 2 σ2 = 4  =&gt; σ = 2

Q: J and K are independent events. P(J | K) = 0.17. Find P(J) P(J) =

A:

Q: J and K are independent events. P(J | K) = 0.76. Find P(J) P(J) =

A: Solution: Independent events: Two events A and B are said to be independent if the happening of one…

Q: X f(x, y) 2 4 1 0.10 0.15 y 3 0.20 0.30 5 0.10 0.15 e. Determine the conditional distribution of f…

A: Farmula used  P(X/Y=y)=P(X,Y=y)/P(Y=y)

Q: 5. Let P be a probability measure and A, B two events. Show that |P(An B) – P(A)P(B)| < . Hìnt: Show…

A:

Q: Use the rules of expectations to show that Var(X + Y ) = Var(X) + Var(Y ) + 2Cov(X,Y )

A: Formula Used: Var(X) = EX2 - EX2                      ............Equation (1) Cov(X, Y) = EXY -…

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: 8 models a continuous probability for 1 < x < 8. 7x2 The function f(x) Compute the median:

A:

Q: Translate the following statements using probability notation. Use X as the random variable. The…

A: Translate the statements using probability notation.

Q: The source is given sample suggestions for probability, and its equivalent in conditional…

A: Given data: The first condition rule is 0≤P(E/G)≤ 1. The second conditional rule is…

Q: Number of cars sold, X Probability, P(X) 0 1 2 3 4 Compute P(1 < X <3). Select one: O a. 0.40 b.…

A:

Q: J and K are independent events. P(J | K) = 0.19. Find P(J) P(J) =

A: Given,     The objective is to find the P(J).

Q: state s probability P(s) realization X(s) realization Y(s) 1 .1 10 20 2 .2 20 30 3 .2 10 10 4 .3 10…

A:

Q: Prove- Assume that X1 ∼ P oi(λ1), X2 ∼ P oi(λ2). Assume also that X1 and X2 are independent.…

A:

Q: Maddy waits tables and has determined that 12% of her tables leave her 12 percent tip, 30% of her…

A: x P(x) xP(x) 12 0.12 1.44 15 0.3 4.5 18 0.48 8.64 20 0.1 2 Total 1 16.58

Q: Find the conditional expectation E(Y|X=1) Find the conditional expectation E(XY = 2)

A: Solution

Q: If (xoy). X 2 4 · 10.10 3 0.15 0.20 0.30 5 0·10 0·15 d. Determine the cumulative distribution…

A: Given data is  f(x,y) x 2 4 Total y 1 0.10 0.15 0.25 3 0.20 0.30 0.50 5 0.10 0.15 0.25…

Q: (b) Pr[X > 0.6n] < 0.85. Let X be the number of HEADS after n fair coin tosses. Show that

A:

Q: find the conditional frequency function of X given that Y =4 , and the conditional frequency…

A: Conditional frequency of X that given that Y = 4 is given as: For X = 3,

Q: Assume that an investor could invest in a risky asset that is expected to earn $150,000 nothing with…

A: The given risky investment can result in two types of returns 150,000 with probability 0.5 And, 0…

Q: Let X have a uniform distribution on the interval [0,1] and let Y ~ N(0,1). Suppose that X and Y are…

A: Here, X ~ Uniform(0,1) Y ~ N(0,1) PDF of X, fXx = 1if 0&lt;x&lt;10otherwise So, CDF of X, FX(x) =…

Q: P(- c ≤ Z ≤ c)=0.9399

A: We have given that  P(- c ≤ Z ≤ c)=0.9399 From the given information we have to find the value of c

Q: Let X have a distribution N(2,4). Calculate P(|x| = <1.2) and P(x| = <11.6) and determine such x for…

A:

Q: A class contains 35 students. The probability of failing in one of the courses for each student is…

A:

Q: The probability that between 3 and 7 automobiles will be sold is,

A:

Q: 5. Let f(x) is probability distribution function of X with: f(x) = { 21, x = 0, 1, 2, 3, 4, х 3 0,…

A: