{"id":2780,"date":"2012-09-26T00:16:41","date_gmt":"2012-09-26T00:16:41","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=2780"},"modified":"2014-12-02T08:32:01","modified_gmt":"2014-12-02T08:32:01","slug":"probability-distribution-random-variables","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/probability-distribution-random-variables\/","title":{"rendered":"Probability Distribution: Random Variables"},"content":{"rendered":"

A random variable is a function which is usually denoted by X<\/em><\/strong> defined on the sample space S<\/em><\/strong> whose range is the set of real numbers.<\/p>\n

i.e. X:S–> R is called a random variable.<\/p>\n

Example:<\/span><\/strong><\/p>\n

If an unbiased coin is tossed,<\/p>\n

Then sample space S={H, T}<\/p>\n

Let\u00a0<\/strong><\/em>X<\/strong><\/em> denoted the number of tails obtained.<\/p>\n

Then X(T)=1 (the number of chances of getting \u2018T\u2019 =1).
\n<\/strong><\/p>\n

Probability\u00a0 distribution:<\/span><\/strong><\/p>\n

The probability distribution of a random variable x is as follows.
\n<\/strong><\/p>\n

\n\n\n\n\n
\n

X = r<\/p>\n<\/td>\n

\n

1<\/p>\n<\/td>\n

\n

2<\/p>\n<\/td>\n

\n

3<\/p>\n<\/td>\n

\n

\u2026\u2026.<\/p>\n<\/td>\n

\n

n<\/p>\n<\/td>\n<\/tr>\n

\n

P(X=r)<\/p>\n<\/td>\n

\n

P(X=1)<\/p>\n<\/td>\n

\n

P(x=2)<\/p>\n<\/td>\n

\n

P(X=3)<\/p>\n<\/td>\n

\n

\u2026\u2026\u2026\u2026..<\/p>\n<\/td>\n

\n

P(X=n)<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\u00a0<\/strong><\/p>\n

Here all probabilities are non \u2013 zero and sum of all probabilities is 1.
\n<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

Example – 1:<\/span><\/strong> <\/strong><\/p>\n

If 2 coins are tossed and X<\/strong><\/em> is the random variable which denotes the number of heads then<\/p>\n

Sample space, S<\/strong><\/em> = {HH,HT,TH,TT}<\/p>\n

n(S) = 4.<\/p>\n

X can be 0,1,2<\/p>\n

P(X=0) = probability of getting zero heads =\u00a0 1\/4 (TT)<\/p>\n

P(X=1) = probability of getting 1 head =\u00a0 2\/4=1\/2 \u00a0(HT,TH)<\/p>\n

P(X=2) = probability of getting 2 heads =\u00a0 1\/4 \u00a0\u00a0(HH)<\/p>\n

 <\/p>\n

So, the probability distribution of X is as follows.<\/p>\n

 <\/p>\n

\n\n\n\n\n
\n

X = r<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

1<\/p>\n<\/td>\n

\n

2<\/p>\n<\/td>\n<\/tr>\n

\n

P(X=r)<\/p>\n<\/td>\n

\n

1\/4<\/p>\n<\/td>\n

\n

1\/2<\/p>\n<\/td>\n

\n

1\/4<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n


\n<\/strong><\/p>\n

Example-2:<\/span><\/strong> <\/strong><\/p>\n

If\u00a0 3 coins are tossed and\u00a0X<\/strong><\/em> is the random variable which denotes the number of heads then<\/p>\n

 <\/p>\n

Sample space, S = {HHH,HHT,HTT,TTT,TTH,THH,HTH,THT}<\/p>\n

n(S) = 8.<\/p>\n

X<\/strong><\/em>\u00a0can be o,1,2,3<\/p>\n

P(X=0) = probability of getting zero heads =\u00a0 1\/8 (TTT)<\/p>\n

P(X=1) = probability of getting 1 head =\u00a0 3\/8 \u00a0(HTT,THT,TTH)<\/p>\n

P(X=2) = probability of getting 2 heads =\u00a0 3\/8 \u00a0(HHT,HTH,THH)<\/p>\n

 <\/p>\n

P(X=3) = probability of getting 3 heads = \u00a01\/8 \u00a0(HHH)<\/p>\n

So, the probability distribution of X is as follows.<\/p>\n

 <\/p>\n

\n\n\n\n\n
\n

X = r<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

1<\/p>\n<\/td>\n

\n

2<\/p>\n<\/td>\n

\n

3<\/p>\n<\/td>\n<\/tr>\n

\n

P(X=r)<\/p>\n<\/td>\n

\n

1\/8<\/p>\n<\/td>\n

\n

3\/8<\/p>\n<\/td>\n

\n

3\/8<\/p>\n<\/td>\n

\n

1\/8<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\u00a0<\/strong><\/p>\n

 <\/p>\n

Do you also need help with Geography? Take a look at our Geography<\/a> tutoring services.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Oshawa visit: Tutoring in Oshawa. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

A random variable is a function which is usually denoted by X defined on the sample space S whose range is the set of real numbers. i.e. X:S–> R is called a random variable. Example: If an unbiased coin is tossed, Then sample space S={H, T} Let\u00a0X denoted the number of tails obtained. Then X(T)=1 […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[15],"tags":[517,3822,1479,1582,1925],"class_list":["post-2780","post","type-post","status-publish","format-standard","hentry","category-probability","tag-distribution","tag-probability","tag-random","tag-sample-space","tag-variable"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/2780","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=2780"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/2780\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=2780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=2780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=2780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}