Given X ~N (25, 52) Find k such that P(20 < x < k) = 0.4 using normal distribution laws
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Given X ~N (25, 52) Find k such that P(20 < x < k) = 0.4 using
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- Let random sample of n observations from each of the distributions: a. Poisson distribution with parameter θ. b. f(x, θ) = (1/ θ) e-x/θ , 0 < x. In each case find the Minimum Variance Estimator of θ and prove its efficiency.Let X,...,X6 be a random sample of size 6 from Normal(0, o2). a. What is the constant "a" so that a (X1-X3) Y = 2x+ $x+x+ x is t-distribution? b. Compute P(Y < 0.95).Let {N(t); t ≥ 0} be a renewal process with the gamma distributed inter- occurrence times with parameters 2 and 3 .The probability distribution of waiting time until the fifteenth renewal occurs is Select one: a normal distribution with paramters 10 and variance 3.33 O b. normal distribution with mean10 and variance 50 gamma distribution with parameters 30 and 3 O d. gamma distribution with parameters 30 and 45 O C.
- Let X be a continuous random variable whose distribution is given by X ~ PAR(6.2). Find the 65th percentile, 65. O 1.2461 O 1.0613 O 1.1229 O 1.1845 O 1.3077Let Zı, Z2, ... Zn represent a random sample of size n from a standard normal distribution. f n= 5; X= Z + Z+ Z and Y=Zi+Zs. What is the distribution of 2X/3Y? (Note: you must either prove or justify your argument using known theorems)When taking random samples of n observations from a population that is not normally distributed, the sampling distribution, x, will be approximately normally distributed never. The population itself must be normally distributed for x to be normally distributed. when the population distribution has low kurtosis. always. when the population standard deviation, o, is greater than n. when n is sufficiently large.
- find oc x is a a normal mean U=3 805-0-5 random distribution P (ocSuppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A n > 30 B The population is normally distributed. C n > 30 OR the population is normally distributed D n > 30 AND the population is normally distributedThe random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630Let zz denote a variable that has a standard normal distribution. Determine the value z∗z∗ to satisfy the following conditions: (a) P(z>z∗)=.7642P(z>z∗)=.7642 (b) P(z<z∗)=.937P(z<z∗)=.937 (c) P(z>z∗orz<−z∗)=0.03The random variable X has expected value E(X)=4 and Var(X)=4. Here, we want to approximate the probability that X lies in the interval [3.4,5.4] using a transformation to a standard normal distribution Z. Then we will need to calculate the probability that Z lies in the interval [z1,z2] where z1= z2= Suggest z1 and z2 Do NOT attempt to make any sort of continuity correction.Q1: Suppose the number of customers X that enter a store between the hours 9:00 a.m. and 10:00 a.m. follows a Poisson distribution with parameter 0. Suppose a random sample of the number of customers that enter the store between 9:00 a.m. and 10:00 a.m. for 10 days results in the values 9, 7, 9, 15, 10, 13, 11, 7, 2, 12 Determine the maximum likelihood estimate of 0. Show that it is an unbiased estimator. Q2: Assume that X is a discrete random variable with pmf f(x). Let X₁,...,X₁ be a random sample on X. Suppose that the space of X is finite, say, D={a₁,...,m}. An intuitive estimate of p(a) is the relative frequency of a, in the sample. We express this more formally as follows. For j=1, 2,..., m, define the statistics 1,(X) = {1 0 X₁ = a; X₁ = a; Then the intuitive estimate of p(a)) can be expressed by the sample average p(a) = -1,(X₂) Find the unbiased estimator and the variance of the estimator and its mgf.
