{"id":2789,"date":"2012-08-08T01:21:21","date_gmt":"2012-08-08T01:21:21","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=2789"},"modified":"2014-12-02T08:32:06","modified_gmt":"2014-12-02T08:32:06","slug":"random-variables-mean-variance-and-standard-deviation","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/08\/08\/random-variables-mean-variance-and-standard-deviation\/","title":{"rendered":"Random Variables: Mean, Variance and Standard Deviation"},"content":{"rendered":"

When determining characteristics of a variable, there are a variety of data points that can be determined. For all of our examples shown today, we will let X<\/strong><\/em> be the random variable with the possible values xi, for i=1,2,\u2026..,n with the corresponding probabilities P(X=xi), i=1,2,,\u2026..n.
\nMean:<\/strong><\/span> <\/strong><\/p>\n

The mean of a random variable is the average of all the possible values of the random variable.<\/p>\n

The series \"\"<\/a>if exists is called the mean of random variable X and it is denoted by \u2018\u00b5\u2019 .<\/p>\n

i.e. Mean, \u00b5 =\"\"<\/a><\/p>\n

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

The variance of a random variable measures the variability (or spread) of the distribution.<\/p>\n

The series \"\"<\/a>if exists is called the variance of a random\u00a0 variable X<\/em><\/strong> and is denoted by\u00a0 \"\"<\/a>\u00a0.<\/p>\n

i.e. Variance,\"\"<\/a><\/p>\n

Standard deviation:<\/span><\/strong> \u00a0<\/span>The non negative number which is the square root of variance is called\u00a0 standard deviation and is denoted by \"\"<\/a>.<\/p>\n

i.e standard deviation, \"\"<\/a><\/p>\n

Example:<\/span><\/strong> \u00a0When 3 coins are tossed, the probability distribution of X<\/em><\/strong> where X<\/em><\/strong> denotes the number of heads is,<\/p>\n

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

X<\/em><\/strong> = 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<\/em><\/strong> =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

\"\"<\/a><\/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 Ottawa visit: Tutoring in Ottawa. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

When determining characteristics of a variable, there are a variety of data points that can be determined. For all of our examples shown today, we will let X be the random variable with the possible values xi, for i=1,2,\u2026..,n with the corresponding probabilities P(X=xi), i=1,2,,\u2026..n. Mean: The mean of a random variable is the average […]<\/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":[4,15],"tags":[487,1096,3822,1721,1927],"class_list":["post-2789","post","type-post","status-publish","format-standard","hentry","category-calculus","category-probability","tag-deviation","tag-mean","tag-probability","tag-standard","tag-variance"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2789","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=2789"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2789\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=2789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=2789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=2789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}