A particle executes an unrestricted simple random walk on the line with p=0.7 and q=0.3. Its position at time n is represented by the random variable Xn, n= 0, 1,...; Xo = 0. (a) Calculate the values of the following probabilities. (i) P(X5 = -2) (ii) P(X6 =2) (b) Calculate the probability that the particle returns to its starting point for the first time after 8 steps. (c) After the particle has been moving for some time, it is observed to be located at the point +3. (i) Calculate the probability that the particle will ever return to the origin from the point +3. (ii) Calculate the probability that starting from the point +3, the particle will visit the point +8 without first visiting the origin.

Q: f x is a binomial random variable, compute p(x) for each of the following cases: (a)  n=3,x=1,p=0.5…

A: a)  n=3,x=1,p=0.5 P(X=1)=3C1 * 0.51*0.53-1 =0.375

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

A: Basic probability

Q: In each part, assume the random variable X has a binomial distribution with the given parameters.…

A: A random variable X~Binomial (n, p)P(X=x)=nxpx(1-p)n-x    ;x=0,1,2.....n

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: Assume that the time of arrival of the birds at a particular place on a migratory route, as measured…

A: The objective of the question is to find the probability that the birds arrive after 160 days but on…

Q: (a) P(x ≤ 4), n = 6, p = 0.9 P(x) = (b) P(x > 5), n = 9, p = 0.6 I P(x) = (c) P(x < 3), n = 4, p =…

A:

Q: a) Find the values of aa and bb. (b) Find the probability at least two students order groceries…

A:

Q: For the random variable X, E(X+1) = 3 , E(X- +X)= 9 then the value of Var(X) is 10 3 0 2 0 50

A: Given, E(X+1)=3 Then E(X)+1=3          E(X) =2 and E(X2+X)=9       E(X2)+E(X)=9       E(X2)+2=9…

Q: x is a binomial random variable. (Give your answers correct to three decimal places.) (a) Calculate…

A:

Q: (1) Let X be a random variable with a function [A(3x² +6) -1,0,1,2 . then (0) k = (6) k = (e) * (d)…

A:

Q: (2) In mathematics department, there are 5 professors, 2 of them are Saudis. Two professors are…

A: Given: Total number of professors (N) = 5 Number of Saudi professors (K) = 2 Number of non Saudi…

Q: The probability of event A, given that event B has occurred, can be found using Bayes' Theorem. P(A)…

A: P(A)=68% P(A')=32% and P(B|A)=43% ane P(B|A')=53%

Q: A bakery shops sells an average of 105 cakes per week (i) Find the probability that on a given day…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Question 6: Circle correct answer choice(s) (i) Let W, X and Y are random variables. Choose the…

A: formulae used E(4X)=4E(X) Var(4X)=16 Var(X) Expectation of a constant=constant i.e. E(4)=4 Variance…

Q: (1)A random variable is defined as 1/36(2x-1); x= 1,2,3,4,5,6     (a)Construct the Probability…

A: Random variable  X defined  as  fx=1362x-1   x=1,2,3,4,5,6∴fi=PX=xi         x1=1, x2=2,x3=3…

Q: x is a binomial random variable. (Give your answers correct to three decimal places.) (a) Calculate…

A: we are suppose to do three sub parts only

Q: Let X be a random variable with the following probability values. f(x) = c(1 – 2x2 + x³), x = 0,1,…

A: Let X be a random variable with the following probability values. fx=c1-2x2+x3,    x=0,1,2,3,4,5 a)…

Q: Jerry is a trickster. He managed to create a coin which has probability of coming up H is p = 0.5304…

A:

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: 1+3x 1-4x (10) If a random variable assumes 4 values with probability 1+1 1+2 and the condition on x…

A: A random variable assumes 4 values with probability p1=1+3x4 , p2=1-x4 , p3=1+2x4 , p4=1-4x4

Q: Question 6: Circle correct answer choice(s). (i) Let W, X and Y are random variables. Choose the…

A:

Q: 1-4x and 4 1+3x 1-x 1+2x (5) If a random variable assumes 4 values with probability the 4 4 4…

A: If the random variable assumes 4 values , then the sum of all probabilities for x should be equal to…

Q: (2) Let X be a random variable with p.d.f. 1<x<10 f(x) = then o.w 3 (a) k=2 (b) k=8 (c) k = (d) k=3…

A: Solution: 2. From the given information, the probability density function of X is

Q: 4 Let X be a discrete random variable with PGF P,(s) = () %3D 3 Find the probability distribution of…

A:

Q: The probabilities of two events A and B are P(A) = 0.5 and P(B) = 0.3 respectively. If P( A U B ) =…

A:

Q: A random variable X can take only the values 0, -5, and 2. It is known that Pr[X 0] = 0.3 and Pr[X =…

A: We have to solve given problem:

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: Assuming that X is a binomial random variable with n = 10 and p = 0.25, find the probability, P for…

A: sample size(n)=10p=0.25

Q: Let X be a random variable that can take values 2, 3, and 5 with probabilities P(X=2)=1/2,…

A: Given  P(X=2)=1/2, P(X=3)=1/4, and P(X=5)=1/4.

Q: Q7 Suppose X and Y are independent exponential random variables with parameters A1 and A,…

A:

Q: Let X be a random variable whose value is in the set {-2, –1,0, 1, 2} with equal probabilities. Let…

A: Ans#- Given X be a random variable  and  X ={ -2, -1, 0, 1, 2 }             Let Y = X  then find…

Q: (7) A random variable X will take one of its possible values (z) as its actual value, its…

A: Given data is xi P(xi) -2 0.1 0 0.2 5 0.2 8 0.3 10 0.2

Q: Assuming that X is a binomial random variable with n = 10 and p = 0.25, find the probability, P for…

A:

Q: For a random variable X with a binomial (20,1/2) distribution, find the following probabilities.…

A: Using R, all 3 parts have been solved using the code given below i) ii)

Q: 2 A discrete random variable Y takes the values -1, 0 and 1 with probabilities 10, 1-0 and 10…

A:

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: x is a binomial random variable. (Give your answers correct to three decimal places.) (d)…

A: d)  n = 5,  x = 1,  p = 0.5 P(X=x) = Cxn×px×1-pn-x P(X=1) = C15×0.51×1-0.55-1 P(X=1)…