.6(a) Two sets of n independent trials are performed, independently of each other, and each trialresults in either success or failure, the probability of success being p₁ in the first set of trials andP2 in the second set. Show that the probability P of obtaining x₁ successes in the first set andx₂ successes in the second set is given byP = Kpip2¹ (1-P₁)"¯*¹(1 - P2)"¯*²,where K depends only on n, x₁ and x₂. If p₁ = p and p₂ = p², find an expression for log Pand show that, for given values of n, x₁ and x2, log P has a maximum value when p is suchthat(x₁+ 2x₂)(n-x₁)p3np² = 0.(b) An insect breeding experiment was conducted in two sections, in each of which 100 insectsof a particular species were raised. In the first section a proportion p was expected to have acertain colour variation and in the second section the proportion with this colour variation wasexpected to be p², but the value of p was not known. In the event there were 22 insects in thefirst section, and 7 in the second section, which possessed the colour variation. Find the valueof p which maximises the probability of this result.

Answered: Image /qna-images/answer/15055464-961c-408a-b19a-ef1aa33dfb4f.jpg

Answered: .6 (a) Two sets of n independent trials…

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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Eight students attended a birthday party. Three of them were confirmed Covid-19 positive. The contact tracer had conducted a random test for only two students. Find the probability distribution for random variable X which represents the number of Covid-19 positive patients. What three statements of the problem can be concluded out of the topic Covid-19?
An electronics store has received a shipment of 20 table radios that have connections for an iPod or iPhone. Ten of these have two slots (so they can accommodate both devices), and the other ten have a single slot. Suppose that six of the 20 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the radios stored under the display shelf that have two slots. (a) What kind of distribution does X have (name and values of all parameters)? O hypergeometric with N = 10, M = 6, and n = 10 O binomial with n = 20, x = 10, and p = 6/20 hypergeometric with N = 20, M = 10, and n = 6 O binomial with n = 10, x = 6, and p = 6/10 (b) Compute P(X= 2), P(X ≤ 2), and P(X ≥ 2). (Round your answers to four decimal places.) P(X = 2) = P(X ≤ 2) = P(X ≥ 2) = (c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.) mean value standard deviation…
It is equally probable that two signals reach a receiver at any instant of the time T. The receiver will be jammed if the time difference in the reception of the two signals is less than T. Find the probability that the receiver will be jammed.
You are allowed to take a certain test three times, and your final score will be the maximum of the test scores. Your score in test k, where k = 1, 2, 3, takes one of the values from k to 10 with equal probability 1/(11 − k), independently of the scores in other tests. What is the PMF of the final score?
In the transmission of digital information the probability that a bit has a high high moderate , and low distortion is 0.01 , 0.04 and 0.95 . suppose that three bits are transmitted and that the amount of distortion of each is assumed to be independent let X and Y denote the number of bits with high and moderate distortion out of the three . what is the range for probability of X and Y
The complement of an event is all possible outcomes not in the event. For example: If A = at least 3 girls are born to a family with 6 kids. Then A' = A compliment is what happens if there are not at least 3 girls = less than 3 girls born to the family. A useful formula: P(A) + P(A' ) = 1 or P(A') = 1 - P(A). If P(A) = 0.194, what is P(A')?
Two bags of crayons contain an assortment of different colours. The probability of randomly selecting a red crayon from the first bag is 4/5. The probability of randomly selecting a red crayon from the first bag and a blue crayon from the second bag is 0.36. The probability, to the nearest hundredth, of selecting a blue crayon from the second bag is:
Q.2 the probability that a missile hit the target is 0.90. If three missile of this type has been fired. Find the probability that (i) at least 2 hit the target. (ii) Exactly two hit the target.
A large bag contains pretzels with 3 different shapes: heart, square, circle . Billy plans to reach into the bag and draw out one pretzel at a time, stopping only when he has at least one pretzel of each type. Let the random variable X denote the number of pretzels that Billy will draw from the bag. You can assume that there is an infinite number of pretzels in the bag with equal proportions of each shape. Find E(X).
Nearly 75% of all deaths in the United States are attributed to just 10 causes, with the top four of these accounting for over 50% of all non-accidental deaths as follows: heart disease (23.4%), cancer (22.5%), respiratory disease (5.6%), and stroke (5.1%).t A study of the causes of n = 307 non-accidental deaths at a local hospital gave the following counts. Heart Respiratory Cause Cancer Stroke Other Disease Disease Deaths 81 80 29 13 104 Do the data provide sufficient information to indicate that the number of deaths at this hospital differ significantly from the proportions in the population at large? Test using the p-value approach. (Use a = 0.05.) State the null and alternative hypotheses. HoiP1 = P2 = P3 = P4 = P5 %D %D : At least one p, is different from Hai Ho: At least one p, is different from the specified value. Ha: P1 0.234; p2 = 0.225; p3 = 0.056; P4 = 0.051; P5 = 0.434 Ho: At least one p; is different from Нai P1 3 Р2 -Р3 — Р4 — P5 Hoi P1 H: No value of p, is the same as…
Suppose we know that 0.1% of the population is infected with COVID-19 (the probability that a randomly selected individual is infected with COVID-19 is 0.001). We have a test for COVID-19 that is 99.9% accurate (if the person is infected, then the probability of being tested as POSITIVE is 0.999; if the person is NOT infected, the probability of being tested as NEGATIVE is 0.999) What is the probability that Draco is actually infected with COVID-19, given that he has tested positive? Hint: Draw the appropriate tree diagram and use Bayes' Theorem.

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