4. The Poisson distribution is an important discrete distribution used to model events that occurwith characteristic rates. It is also the underlying statistical model for regression techniquesinvolving categorical data. The pmf of the Poisson distribution is given by:ake-2P(X = k)k!a) Show that the mean/expected value of this distribution is given by:E(X) = 1b) Show that the variance of this distribution is given by:Var(X) = E(X²) – (E(X))² = 1

a) Expected value:The expected value is given below:

Answered: 4. The Poisson distribution is an…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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BUS – 173 (Applied Statistics) # Determining if the following statement are True and False. If False, write the correct statement. Also Solve the MCQ 01. In the Simple linear regression model, components of the random error term are assumed to be independent (a) True (b) False 02. The possible for the perfect negative correlation is +1 (a) True (b) False 03. The possible range of coefficient of determination (r^2) is -1 to 1 a) True (b) False 04. A scatter diagram is a - (a) two-dimensional graph of a straight line (b) two-dimensional graph of a curved line (c) two-dimensional graph of a data points (d) one-dimensional graph of randomly scattered data
Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately ?2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 41 women in rural Quebec gave a sample variance s2 = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom?
Q 1 If X is a random variable with distribution X: 0 1 2 3 P(X): 1111 44 44 Find the mean, Variance and standard deviation. Q 2 If X is a random variable with distribution X: 0 12 3 4 P(X): 0 K 2K 3K 4K Explain the following: (i) For which value of K, P(X) is probability mass function? (ii) Find the following probabilities: (a) P(1 ≤ X < 4). (b) P(2 < X < 4). Q3 A box contains 6 balls. Two are numbered 4, two are numbered 5, and two are numbered 6. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the variance (²) and standard deviation (o) of the numbers on the balls. Q4 A special six-sided die is made in which 2 sides have 6 spots, 3 sides have 4 spots, and 1 side has 1 spot. If the die is rolled, find the expected value of the number of spots that will occur. Q5 Let X-B(4,0.6). Find the following (i) P(X = 2) (ii) P(1 < X < 4) (iii) Also find mean and variance. Q6…
If Y is Normally distributed , and p(y < 170 ) = 0.14 p ( y > 200 ) = 0.03 then the values of the mean and variance of Y , respectively are
Scores on a certain exam are normally distributed with a mean of 90 and a variance of 25. What is the z-value for a score of 80? -2.0 -0.4 1.0 2.0 0.4
In a trivariate distribution the simple coefficient of correlation are as follows if r12 = 0.76, rı3= 0.75 and r²3= 0.71 calculate the coefficient of partial correlation r 12.3
Answer all
Q.No.1. (Marks 08) Explain the following with suitable examples. Mutually exclusive events Sampling Correlation Regression
Can you please help me with parts C, E, and F?
just please answer the sub-b
Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s2 = 3.4. Use a 5% level of significance to test the claim that the current variance is less than 5.1. (a) What is the level of significance? State the null and alternate hypotheses. H0: σ2 < 5.1; H1: σ2 = 5.1H0: σ2 = 5.1; H1: σ2 < 5.1 H0: σ2 = 5.1; H1: σ2 > 5.1H0: σ2 = 5.1; H1: σ2 ≠ 5.1 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a exponential population distribution.We assume a normal population distribution. We assume a uniform population distribution.We assume a binomial population distribution. (c) Find or estimate the P-value…

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