Is this a binomial distribution? Х 0 1 2 3 P(x) 0.343 0.441 0.189 0.027 Send...
a) Consider the following data on a variable that has Bernoulli distribution: X P (X) 0 0.3 1 0.7 Find the Expected value and the variance of X. And E(X)-X Px) b) Consider the following information for a binomial distribution: N number of trials or experiments 5 x- number of success 3 Probability of success p 0.4 and probability of failure 1-p 0.6 Find the probability of 3 successes out of 5 trials: Note P(x) Nox p* (1-p)Note: NcN!x! (N-x)!...
1) Binomial distribution, f(x) = px (1 – p) n-x , x = 0, 1, 2, …, n n = 10, p = 0.5, find Probabilities a) P(X ≥ 2) b) P(X ≤ 9) 2) f(x) = (2x + 1)/25, x = 0, 1, 2, 3, 4 a) P(X = 4) b) P(X ≥ 2) c) P(X ≥ -3) 3) Z has std normal distribution, find z a) P(-1.24 < Z < z) = 0.8 b) P(-z < Z <...
Let X be random variable with the binomial distribution with parameters n and 0 < p < 1. (1) Show that (P(X = x) / P(X = x -1)) - 1 = np + (p - x)) / (x(1-p)) for any 1 ≤ x ≤ n. (2) Show that when 0 ≤ x < (n + 1)p , P(X = x) is an increasing function x and for (n + 1)p < x ≤ n, P(X = x) is a...
Suppose X is a binomial distribution with parameters n and p. Find the Bias and MSE of the following estimators for p (а) Өт (b) Ө2 (c) For which values of p is MSE(e1) < MSE(e2)? х X+1 n+2
QUESTION 4 Find the mean of the distribution shown. Х P(x) 0 0.26 5 3 0.24 0.50 2.50 2.24 3.22 3.48 QUESTION 5 Find the mean of the distribution shown. х P(X) -3 0.18 -2 0.24 - 1 0 0.41 0.17 0 -1.74 O -1.43 0 -1.95 O 1.95
f(31–43 10.320.72 543 Computing Binomial Probabilities If X is a binomial random variable with parameters n and p, the probability distribution of Xis given by f(k) = P(X=k) = (pkan* for k =0, 1. , .,where q=1-p. Example: Suppose n = 5 and p = 0.3. Then q = 1 - p = 0.7, f(k)= 10.3)* (0.75% f(0)=C6 20.3)%0.7)-1-1-(0.16807)-0.16807. f(1)=( )(0,3)(0.7) 10.3)(0.2401) - 5(0.07203)0.36015 0 0.1681 f(2)=(3 10.3)2(0.73 (0.09)(0.343) – 10(0.03087)-0.30870 1 0.3602 0.027)(0.49) =10(0.01323)-0.132302 0.3087 f(4)=( )(0.3)*(0.7) (0.0081)(0.7) -5(0.00567)=0.0284...
Suppose that x has a binomial distribution with n = 198 and p = 0.44. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (o) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x пр n(1 - p) Both np and n(1 – p) (Click to select) A 5...
3 (17') The random variable X obeys the distribution Binomial(n,p) with n=3, p=0.4. (a) Write Px(x), the PMF of X. Be sure to write the value of Px(x) for all x from - to too. (b) Sketch the graph of the PMF Px [2] (c) Find E[X], the expected value of X. (d) Find Var[X], the variance of X.
Suppose that x has a binomial distribution with n = 200 and p = 0.42. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (o) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x. np n(1 – p) Both np and n(1 – p) (Click to select) A 5...
х P 0 .2645 1 .3518 2 .2339 os 3 2074 X 4 2065 х 5 .2208 X 0 6 or more .243976 X For a recent period of 100 years, there were 133 major earthquakes in a particular region. Assuming that the Poisson distribution is a suitable model, find the mean number of major earthquakes per year. mean = 1.33 Now, find the probablity distribution for the number of earthquakes in a randomly selected year, rounding each probability to...