If the random variable X is uniformly distributed over I V3 сотрute V3 30 and compare it with the upper bound obtained by Chebyshev's inequality.
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- An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.The number of offspring of an organism is a discrete random variable withmean μ and variance σ^2. Each of its offspring reproduces in the same manner. Find the expected number of offspring in the third generation and its variance.Suppose x binom(6, p) and define estimator T=x/6to estimate p. Then, variance of t is
- Suppose X~ Binom (6,p) and define an estimator T=X/6 to estimate p. Then variance of T isIn this question, you will explore a new distribution called the uniform distri- bution and use R to conduction a simulation that demonstrates how the CLT works. A uniform random variable is a continuous random variable which PDF looks like a rectangle. It has two parameters: 1) a which specifies the minimum value of the random variable, and 2) b which specifics the maximum value of the random variable. We usually denote a uniform random variable X as X~ Uniform(a, b). In R, the runif() function can be used to generate data from the uniform distribution. In runif (), the default values for parameters a and b are 0 and 1. Read the help page for runif () and perform the following: (a) Generate 1000 data points from Uniform(0, 1). Attach your code. (b) Use hist() function to draw a histogram of the 1000 data points you generated in part (a). Describe the shape of the histogram in words. Attach the code and the histogram. (c) Now we will use demonstrate how the CLT works. Generate 30 data…The spinner is spun one fime and a fair coin is tossed. Find the probabilities. P(R) = P(T) = %3D Yellow Red P(B U T)= P(G^) = Blue Green Sample Space: P(G N H)= P(Y U H)C = P(BC)= P(G NT)=
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