{"id":13081,"date":"2024-03-12T12:14:55","date_gmt":"2024-03-12T06:44:55","guid":{"rendered":"https:\/\/tsboardsolutions.in\/?p=13081"},"modified":"2024-03-13T17:35:05","modified_gmt":"2024-03-13T12:05:05","slug":"ts-inter-2nd-year-maths-2a-random-variables-and-probability-distributions-important-questions","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.in\/ts-inter-2nd-year-maths-2a-random-variables-and-probability-distributions-important-questions\/","title":{"rendered":"TS Inter 2nd Year Maths 2A Random Variables and Probability Distributions Important Questions"},"content":{"rendered":"

Students must practice these\u00a0TS Inter 2nd Year Maths 2A Important Questions<\/a> Chapter 10 Random Variables and Probability Distributions to help strengthen their preparations for exams.<\/p>\n

TS Inter 2nd Year Maths 2A Random Variables and Probability Distributions Important Questions<\/h2>\n

Question 1.
\nA cubical die is thrown. Find the mean and variance of X, giving the number on the face that shows up.
\nSolution:
\nLet S be the sample space and X be the random variable associated with S, where P(X) is given by the following table.
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 2.
\nThe probability distribution of a random variable X is given below:
\n\"TS
\nFind the value of k and the mean and variance of X.
\nSolution:
\n\"TS<\/p>\n

Question 3.
\nIf x is a random variable with probability distribution p(X=k)=\\(\\frac{(k+1) c}{2^k}\\) k = 0,1,2 ………… then find c.
\nSolution:
\nSince p(X=k)=\\(\\frac{(k+1) c}{2^k}\\) k = 0,1,2 ……….. is the probability distribution of x
\n\"TS<\/p>\n

Question 4.
\nLet X be a random variable such that
\nP(x=-2) = P(X = -1) = P(X=2)
\nP(X = 1) = \\(\\frac{1}{6}\\) and P(X = 0) \\(\\frac{1}{3}\\)
\nFind the mean and variance of X.
\nSolution:
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 5.
\nTwo dice are roiled at random. Find the probability distribution of the sum of the numbers on them. Find the mean of the random variable.
\nSolution:
\nWhen two dice are rolled, the sample space S consists of 6 x 6 = 36 sample points
\nS = ((1, 1), (1, 2), (1, 6), (2, 1), (2, 6),(6, 6)).
\nLet X denote the sum of the numbers on the two dice. Then the range of X = {(2, 3, 4 , 12)}
\nThe probability distribution for X is given here under:
\n\"TS<\/p>\n

Question 6.
\n8 coins are tossed simultaneously. Find the probability of getting atleast 6 heads.
\nSolution:
\nIn the experiment of tossing a coin, the probability of getting a head \\(\\frac{1}{2}\\) and the probability of getting a tail \\(\\frac{1}{2}\\). The probability of getting r heads in a random throw of 8 coins is
\n\"TS<\/p>\n

Question 7.
\nThe mean and variance of a binomial distribution are 4 and 3 respectively. Fix the distribution and find P(X\u22651).
\nSolution:
\nHere x = B(n,p) is specified by np = 4 = \u03bc and npq = \u03c32<\/sup> = 3
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 8.
\nThe probability that a person chosen at random is left handed (in hand wilting) is 0.1. What is the probability that in a group of 10 people, there is one who is left handed.
\nSolution:
\nHeye n = 10, find p =\\(\\frac{1}{10}\\) = 0.1.
\nHence q = 0.9
\nWe have to find P(X = 1); the probability that
\nexactly one out of 10 is left handed
\nP(X = 1) = 10<\/sup>C1<\/sub> p1<\/sup> q10-1<\/sup>
\n= 10 x 0.1 x (0.9)9<\/sup> = (0.9)9<\/sup><\/p>\n

Question 9.
\nIn a book of 450 pages, there are 400 typo graphical errors. Assuming that the number of errors per page follow the Poisson law, find the probability that a random sample of 5 pages will contain no typo graphical error.
\nSolution:
\nThe average number of errors per page in the book is \\(\\lambda=\\frac{400}{450}=\\frac{8}{9}\\)
\nThe probability that there are r errors per page:
\n\"TS
\nHence P(X=0) = e-8\/9<\/sup>
\nThe required probability that a random sample of 5 pages will contain no error is [P(X) = 0)]5<\/sup> = (e-8\/9<\/sup>)5<\/sup><\/p>\n

Question 10.
\nThe deficiency of red cells In the blood cells is determined by examining a specimen of blood under a microscope. Suppose a small fixed volume contains on an average 20 red cells for normal persons. Using the Poisson distribution, find the probability that a specimen of blood taken from a normal person will contain less than 15 red cells.
\nSolution:
\nHere \u03bb = 20.
\nLet P(X = r) denote the probability that a specimen taken from a normal person will contain r red cells.
\nThen we have P(X < 15)
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 11.
\nA Poisson variable satisfies P(X = 1) = P(X = 2). Find P(X = 5).
\nSolution:
\n\"TS<\/p>\n","protected":false},"excerpt":{"rendered":"

Students must practice these\u00a0TS Inter 2nd Year Maths 2A Important Questions Chapter 10 Random Variables and Probability Distributions to help strengthen their preparations for exams. TS Inter 2nd Year Maths 2A Random Variables and Probability Distributions Important Questions Question 1. A cubical die is thrown. Find the mean and variance of X, giving the number … Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/13081"}],"collection":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/comments?post=13081"}],"version-history":[{"count":2,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/13081\/revisions"}],"predecessor-version":[{"id":13137,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/13081\/revisions\/13137"}],"wp:attachment":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/media?parent=13081"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/categories?post=13081"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/tags?post=13081"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}