{"id":29308,"date":"2024-10-24T07:01:22","date_gmt":"2024-10-24T01:31:22","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=29308"},"modified":"2024-10-25T10:30:04","modified_gmt":"2024-10-25T05:00:04","slug":"samacheer-kalvi-12th-maths-guide-chapter-11-ex-11-4","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-12th-maths-guide-chapter-11-ex-11-4\/","title":{"rendered":"Samacheer Kalvi 12th Maths Guide Chapter 11 Probability Distributions Ex 11.4"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide<\/a> Pdf Chapter 11 Probability Distributions Ex 11.4 Textbook Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.4<\/h2>\n

Question 1.
\nFor the random variable X with the given prob-ability mass function as below, find the mean and variance.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer
\nVar(X)= E(X\u00b2) – [E(X)]\u00b2
\n= 8.1 – (2.3)\u00b2
\n= 8.1 – 5.29
\n= 2.81
\n\"Samacheer
\nVar (X) = E(X\u00b2) – [E(X)]\u00b2
\n= 3.33 – (1.67)\u00b2
\n= 3.33 – 2.79
\n= 0.54
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\nVar (X) = E(X\u00b2) – [E(X)]\u00b2
\n= 8 – 4
\n= 4<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nTwo balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X.
\nSolution:
\nLet X be the random variable that denotes the number of red balls.
\nX = {0, 1, 2}
\nSample space consist of 7<\/sup>C2<\/sub> = 21
\nX= 0, X-1<\/sup> (BB) = 3<\/sup>C2<\/sub>
\nX= 1, X-1<\/sup> (BR) = 3<\/sup>C1<\/sub> \u00d7 4<\/sup>C1<\/sub> = 12
\nX = 2, X-1<\/sup> (RR) 4<\/sup>C2<\/sub> = 6
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nIf \u00b5 and \u03c3\u00b2 are the mean and variance of the discrete random variable X and E(X + 3) = 10 and E(X + 3)\u00b2 = 116, find \u00b5 and \u03c3\u00b2
\nSolution:
\nGiven E(X + 3) = 10
\nE(aX + b) = aE(X) + b
\nE(X + 3) = 10 \u21d2 E(X) + 3 = 10
\n\u21d2 \u00b5 = E(X) = 7
\nE(X + 3)\u00b2 = 116
\nE(X\u00b2 + 6X + 9) = 116
\nE(X\u00b2) + 6E(X) + 9 = 116
\nE(X\u00b2) + 6(7) + 9 = 116
\nE(X\u00b2) = 65
\n\u03c3\u00b2 = Var (X) = E(X\u00b2) – [E(X)]\u00b2
\n= 65 – 49
\n= 16<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nFour fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred.
\nSolution:
\nLet X be the random variable that denotes the number of heads when four coins are tossed once.
\nX ={0, 1, 2, 3}
\nn(S) = 16
\n\"Samacheer
\nVar (X) = E(X\u00b2) – [E(X)]\u00b2
\n= 5 – 4
\n= 1<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nA commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is
\n\"Samacheer
\nObtain and interpret the expected value of the random variable X.
\nSolution:
\n\"Samacheer
\nThe average waiting time for the student is 15 minutes.<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nThe time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function
\n\"Samacheer
\nFind the expected life of this electronic equipment.
\nSolution:
\n\"Samacheer
\nExpected life of the electronic equipment = \\(\\frac { 1 }{ 3 }\\)<\/p>\n

\"Samacheer<\/p>\n

Question 7.
\nThe probability density function of the random variable X is given by
\n\"Samacheer
\nfind the mean and variance of X.
\nSolution:
\nMean:
\n\"Samacheer
\nVar (X) = E(X\u00b2) – [E(X)]\u00b2
\n\\(\\frac { 3 }{ 8 }\\) – \\(\\frac { 1 }{ 4 }\\)
\n= \\(\\frac { 1 }{ 8 }\\)<\/p>\n

\"Samacheer<\/p>\n

Question 8.
\nA lottery with 600 tickets gives one prize of Rs 200, four prizes of Rs 100 and six prizes of Rs 50. If the ticket costs is Rs 2, find the expected winning amount of a ticket.
\nSolution:
\nLet X be the random variable denotes the amount win in the lottery
\n\"Samacheer
\n= 0.5
\nLoss = Rs 0.5<\/p>\n

\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide Pdf Chapter 11 Probability Distributions Ex 11.4 Textbook Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.4 Question 1. For the random variable X with the given prob-ability mass function as below, find the mean and variance. Solution: Var(X)= …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[5],"tags":[],"class_list":["post-29308","post","type-post","status-publish","format-standard","hentry","category-class-12"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/29308"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=29308"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/29308\/revisions"}],"predecessor-version":[{"id":41447,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/29308\/revisions\/41447"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=29308"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=29308"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=29308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}