Consider the discrete random variable X given in the table below. Calculate the mean, variance, and standard deviation of X. Also, calculate the expected value of X. Round solution to three decimal places, if necessary.
x | 4 | 6 | 7 | 10 | 11 | 12 | 19 |
---|---|---|---|---|---|---|---|
P(x) | 0.14 | 0.08 | 0.14 | 0.08 | 0.11 | 0.32 | 0.13 |
μ=
σ2=
σ=
What is the expected value of X ?
E(X)=
Consider the discrete random variable X given in the table below. Calculate the mean, variance, and...
Consider the discrete random variable X given in the table below. Calculate the mean, variance, and standard deviation of X. X 2 3 8 10 16 18 20 P(X) 0.13 0.11 0.37 0.08 0.13 0.09 0.09 μ = σ2 = σ = What is the expected value of X? (All answers should be rounded to one more decimal place than the raw data.) (Remember to perform all calculations before rounding to avoid a rounding error.)
A discrete random variable X has the following probability distribution: x7778798081 P(x) 0.150.150.200.400.10Compute each of the following quantities. i. P(X = 80) ii. P(x > 80) iii. P(X ≤ 80) iv. The mean, μ of x. v. The variance, σ2 of X. vi. The standard deviation, σ of X.
. Suppose that Y is a normal random variable with mean µ = 3 and variance σ 2 = 1; i.e., Y dist = N(3, 1). Also suppose that X is a binomial random variable with n = 2 and p = 1/4; i.e., X dist = Bin(2, 1/4). Suppose X and Y are independent random variables. Find the expected value of Y X. Hint: Consider conditioning on the events {X = j} for j = 0, 1, 2. 8....
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x-36-26-15-4P(X=x)0.320.360.210.11MeanVarianceStandard deviation
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x −36 −26 −15 −4 P(X = x) 0.32 0.36 0.21 0.11 Calculate the mean, variance, and standard deviation
Consider the following discrete probability distribution. x P(x) 1 0.25 2 0.30 3 0.45 Calculate the expected value, variance, and standard deviation of the random variable. Let y=x+5. Calculate the expected value, variance, and standard deviation of the new random variable. What is the effect of adding a constant to a random variable on the expected value, variance, and standard deviation? Let z=5x. Calculate the expected value, variance, and standard deviation of the new random variable. What is the effect...
Let X = (X1, . . . , Xn) be a random sample of size n with mean μ and variance σ2. Consider Tm i=1 (a) Find the bias of μη(X) for μ. Also find the bias of S2 and ỡXX) for σ2. (b) Show that Hm(X) is consistent. (c) Suppose EIXI < oo. Show that S2 and ỡXX) are consistent. Let X = (X1, . . . , Xn) be a random sample of size n with mean μ...
Suppose that X is a standard normal random variable with mean 0 and variance 1 and that we know how to generate X. Explain how you would generate Y from a normal density with mean μ and variance σ"? That is, given that we already generated a random variate X from N(0,1), how would you convert X into Y so that Y follows N (μ, σ 2)?
X is a Discrete Random Variable that can take five values Given The five possible values are: x1 = 4 (Units not given) X2 = 6 (Units not given) X3 = 9 (Units not given) X4 = 12 (Units not given) X5 = 15 (Units not given) The associated probabilities are: p(x1) = 0.14 (Unitless) p(x2) = 0.11 (Unitless) p(x3) = 0.10 (Unitless) p(xx) = 0.25 (Unitless) Question(s) 1. If the five values are collectively exhaustive, what is p(x5)? (Unitless)...
Let X,,X.X be a random sample of size n from a random variable with mean and variance given by (μ, σ2) a Show that the sample meanX is a consistent estimator of mean 1(X-X)2 converges in probability Show that the sample variance of ơ2-02- b. 1n to Ơ2 . Clearly state any theorems or results you may have used in this proof. Let X,,X.X be a random sample of size n from a random variable with mean and variance given...