Question:

Assume you have two boxes An and B. Box A contains 7 dark marbles, 4 white marbles. Box B contains 7 white and 4 dark marbles. An arbitrary test is acted in two consecutive preliminaries by first drawing a marble arbitrarily from enclose An and putting to Box B. In the second preliminary after the principal preliminary, a marble is drawn arbitrarily from box B.

Answer the accompanying inquiries.

Are the two preliminaries autonomous or subordinate? Offer motivations to help your response

Draw a likelihood tree outline to show the execution of this arbitrary trial.

What is the likelihood of drawing a white marble from box B toward the finish of second preliminary?

What is the likelihood of drawing a dark marble from box B toward the finish of second preliminary?

Distinguish every one of the totally unrelated occasions present in the given situation and check that they

are fundamentally unrelated.

In the event that we switch the situation, what is the likelihood of drawing a dark marble from

box A given that a white marble is drawn from box B.

Toward the finish of summer, the complete load of seeds aggregated by a home of seed-assembling insects will fluctuate from one home to another. On the off chance that the normal all out weight of seeds assembled by an arbitrarily picked home is 5 pounds, and the standarddeviationis0.5pounds,whatistheprobabilitythatthetotalcombinedweightoftheseedsgatheredby100 homes will be bigger than 495 pounds before the finish of the following summer? To respond to this inquiry most precisely, given the data accessible, we would utilize:

(8)

1. Chebyshev's hypothesis 2.Markov's hypothesis (3.The Central Limit Theorem 4.The joint likelihood that the heaviness of seeds is bigger than 5 pounds in each home.

Assume you have two boxes An and B. Box A contains 7 dark marbles, 4 white marbles. Box B contains 7 white and 4 dark marbles. An arbitrary test is acted in two successive preliminaries by first drawing a marble haphazardly from enclose An and putting to Box B. In the second preliminary after the principal preliminary, a marble is drawn haphazardly from box B.

Answer the accompanying inquiries.

What is the likelihood of drawing a dark marble from box B toward the finish of second preliminary?

Distinguish every one of the totally unrelated occasions present in the given situation and check that they are totally unrelated.

Assuming we invert the situation, what is the likelihood of drawing a dark marble from box A given that a white marble is drawn from box B.

Assume in a class there are 170 understudies. Of those 170 understudies, 90 are guys and 80 are females. Among 90 male understudies, 55 like playing the sport of football and 35 don't care for it. Among 80 female understudies, 10 like playing the sport of football and 70 don't care for it.

Address this data as a cross classification or likelihood possibility table.

1. If p is the probability of 'successes' at a single trial, obtain the probability of r 'successes' out of n independent trials. 2. Discuss the nature of mode of binomial distribution. 3. Show that if np be a whole number, the mean of the binomial distribution coincides with the greatest term. 4. Obtain the m.g.f. of the binomial distribution. Hence or otherwise obtain the mean, variance and skewness of distribution. 5. State and prove the reproductive property of the Poisson distribution. Show that the mean and variance of the Poisson distribution are equal. Find the mode of the Poisson distribution with mean value 5. 6. Show that for a Poisson distribution, the coefficient of variation is the reciprocal of the standard deviation. 7. If X1, X2. .... Xk are independent random variables following the Poisson law with parameter M1, M2. .... my respectively, show that _=1 X; follows the Poisson law with parameter _ _, mi. 8. Prove the recurrence relation between the moments of Poisson distribution: Hr+1 = 1 (rur-1 + "er), v ax ), where u is the rth moment about the mean A. Hence obtain the skewness and kurtosis of Poisson distribution. 9. Let X has a Poisson distribution with parameter) > 0. If r is a non-negative integer and if ur'= E(X'), prove that #'7+1 = 2 (1, + ) 10. Obtain the Poisson distribution as a limiting case of the negative binomial distribution.Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed. how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? A researcher claims that the standard deviation of the lite of a certain type of lawn mower is at most 2.3 years. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim '2 a statement of equality, it represents the I: hypothesis. contains does not contain Determine whether the claim stated below represents the null hypothesis or the altematiye hypothesis. Ifa hypothesis testis performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypolhesis? A researcher claims that more than 33% of people had at least one health care visit in the past year. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim E a statement of equality. it represents the I: hypothesis. Determine whether the claim stated below represents the null hypothesis or the altematiye hypothesis. If a hypothesis test is performed. how should you interpret a decision that {a} rejects the null hypothesis or (b) fails to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species 01 bird is less than 32 days. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim E a statement ofequality, it represents the l: hypothesis. null alternative Karim's Furniture uses variance analysis to evaluate manufacturing overhead in its table factory. The company uses direct labor (DL) hours to allocate MOH costs. The information for overhead expenditures during the month of May is as follows: Static budgeted output units 14,000 tables Static budgeted FMOH $22,400 Application rate for VMOH $3.00 per DL hour Application rate for FMOH Standard quantity of DL hours per table 0.2 hours Actual Results: Fixed manufacturing costs incurred $24,000 Direct manufacturing labour hours used 4,000 hours Variable manufacutring costs incurred $11,000 Actual units manufactured 15,000 tables Calculate the VMOH spending variance.7.7 Refer to exercise 2.3 concerning the distribution of ant lion pits. Using the sample mean as the best estimate of the parametric mean, deter- mine if the distribution of pits follows a Poisson distribution. Interpret your results biologically. (Note: When determining the Poisson distribu- tion carry out x until the cumulative probability equals 1. Use a statistical program to determine the Poisson Distribution.) Number of Quadrats Pits/Quadrat (X) Containing X Pits (Frequency) 5 15 23 DO YOUTAWNHO