1. Random Walk: Consider a random walk described by the following probability rules: P(+x) 0.5; P...
1-D Random Walk: Consider a random walk described by the following probability rules: P(+x) = 0.5; P(-x) = 0.1 ; P(ty) = 0.2; P(-y) = 0.2 (a) Is the walk biased? If so in which direction? Explain. (b) Compute the following for N steps if the step size is equal to a: <x, y>, <x>, <y'> (c) After long time (after large number of steps, where would the object be found? (find Ox, Ox I. 1-D Random Walk: Consider a...
2) Consider a random variable with the following probability distribution: P(X = 0) = 0.1, P(X=1) =0.2, P(X=2) = 0.3, P(X=3) = 0.3, and P(X=4)= 0.1. A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated...
python / visual studio Problem 1: Random Walk A random walk is a stochastic process. A stochastic process is a series of values that are not determined functionally, but probabilistically. The random walk is supposed to describe an inebriated person who, starting from the bar, intends to walk home, but because of intoxication instead randomly takes single steps either forward or backward, left or right. The person has no memory of any steps taken, so theoretically, the person shouldn't move...
python / visual studio Problem 1: Random Walk A random walk is a stochastic process. A stochastic process is a series of values that are not determined functionally, but probabilistically. The random walk is supposed to describe an inebriated person who, starting from the bar, intends to walk home, but because of intoxication instead randomly takes single steps either forward or backward, left or right. The person has no memory of any steps taken, so theoretically, the person shouldn't move...
2. Consider a random variable with the following probability distribution: P(X=0) = 0.1, P(X=1) = 0.2, P(X=2) = 0.4, and P(X=3) = 0.3 a. Find P(X<=1) b. Find P(1<X<=3)
LSM 5 Part C. Suppose that you are walking on a straight line. You start at position X, -0, and only walk in the positive direction. Your positions afcer taking the ith step is denoted by X,. For each step, your step size, denoted by S, = X,-X,-ı , is a random variable uniformly distributed between 1 foot and 2 eet. Assume that sizes of different steps are mutually independent. 8. (10 credits) Let Xy be your position after taking...
LSM 5 Part C. Suppose that you are walking on a straight line. You start at position Xo , and only walk in the positive direction. Your positions after taking the ith step is denoted by X,. For each step, your step size, denoted by S, . X,-X,-ı , is a random variable uniformly distributed between 1 foot and 2 feet. Assume that sizes of different steps are mutually independent 8. (10 credits) Let X, be your position after taking...
For two bivariate normal random variables X~N(0,1), Y~N(5,1), and CovX,Y=-0.5, answer the following questions: Compute P(Y>5|X=1) Compute P(Y>5|X=-1) Explain why the computed probability in b is greater than that in a. Compute P(2X-Y>-3).
5 Consider a discrete random variable X with the probability mass function rp(x) Consider Y = g( X ) =- 0.2 0.4 0.3 0.1 a) Find the probability distribution of Y. b Find the expected value of Y, E(Y). Does μ Y equal to g(Hy )? 4
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...