Problem 3 Consider the random variable X of the previous question. a. Find the probability distribution...
Q7. (2096) Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. Assume that the coin is biased so that a tail is twice as likely to occur as a head.List the elements of the sample space for the three tosses of a coin and to each sample point assign a value w of a) Find the probability distribution (p.m.f) of the random variable w. b) Find the...
Need help with this Problem 4 A discrete random variable X follows the geometric distribution with parameter p, written X ~Geom(p), if its distribution function is fx(x) = p(1-p)"-1, xe(1, 2, 3, . . .} The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that Ix(z) is indeed a probability inass function, i.e., the sum over all possible values of z is one...
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3, 4, 5, 6} and the following incomplete cumulative distribution function (c.d.f.): 0 0.1 1 0.2 2 ? 3 0.2 4 0.5 5 0.7 6 ? F(x) (a) Find the two missing values in the above table. (b) Let Y = (X2 + X)/2 be a new random variable defined in terms of X. Is Y a discrete or continuous random variable? Provide the probability...
Q–2: [5+2+3 Marks] Let X be a random variable giving the number of heads minus the number of tails in three tosses of a coin. a) Find the probability distribution function of the random variable X. b) Find P(−1 ≤ X ≤ 3). c) Find E(X).
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF Problem 5. Let X...
A discrete random variable X follows the geometric distribution with parameter p, written X ∼ Geom(p), if its distribution function is A discrete random variable X follows the geometric distribution with parameter p, written X Geom(p), if its distribution function is 1x(z) = p(1-P)"-1, ze(1, 2, 3, ). The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that fx(x) is indeed a probability...
Please answer the question clearly 1. Find the probability distribution (PMF) of Y, denoted by f(y), where Y is the absolute differ- ence between the number of heads and the number of tails obtained in four tosses of a balanced coin 2. Determine whether the function f(x) is a valid probability distribution (PMF) for a random variable with the range r - 0,1,2,3, 4. r2 f()30 3. Suppose X is a random variable with probability distribution (PMF) given by f(x)...
Write code that when you are given the range and probability distribution of a random variable X. (i.e X ="the number of heads showing on 2 flipped fair coins": range = (0,1,2) probability distribution: [.25, .5, .25] Such that the code returns the expected value, standard deviation, and variance of the random variable . thanks!
Consider the experiment of tossing a fair coin four times. If we let X = the number of times the coin landed on heads then X is a random variable. Find the expected value, variance, and standard deviation for X.
2. SUPPLEMENTAL QUESTION 1 (a) Toss a fair coin so that with probability pheads occurs and with probability p tails occurs. Let X be the number of heads and Y be the number of tails. Prove X and Y are dependent (b) Now, toss the same coin n times, where n is a random integer with Poisson distribution: n~Poisson(A) Let X be the random variable counting the number of heads, Y the random variable counting the number of tails. Prove...