{"id":7647,"date":"2021-10-13T21:51:19","date_gmt":"2021-10-13T21:51:19","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/pstat-109-quiz-3-winter-2014\/"},"modified":"2021-10-13T21:51:19","modified_gmt":"2021-10-13T21:51:19","slug":"pstat-109-quiz-3-winter-2014","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/pstat-109-quiz-3-winter-2014\/","title":{"rendered":"Pstat 109: quiz 3 winter 2014"},"content":{"rendered":"
\n

PSTAT 109: Quiz 3<\/p>\n

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Winter 2014<\/p>\n

Instructions: Please show all work in an organized fashion for full credit.<\/p>\n

Problem 1. <\/span>Let = <\/span>f<\/span>1<\/span>; <\/span>2<\/span>; <\/span>3<\/span>g<\/span>, and consider the family of subsets <\/span>A <\/span>of :<\/span><\/p>\n

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A <\/span>= <\/span>f;<\/span>;; <\/span>f<\/span>1<\/span>; <\/span>2<\/span>g<\/span>; <\/span>f<\/span>2<\/span>; <\/span>3<\/span>g<\/span>; <\/span>f<\/span>2<\/span>g<\/span>; <\/span>f<\/span>1<\/span>; <\/span>3<\/span>gg<\/span>:<\/span><\/p>\n

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Explain why <\/span>A <\/span>is <\/span>not <\/span>a sigma-algebra.<\/span><\/p>\n

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Problem 2. <\/span>If <\/span>A <\/span>and <\/span>B <\/span>are subsets of sample space , show that<\/span><\/p>\n

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P<\/span>(<\/span>A <\/span> <\/span>B<\/span>) <\/span> <\/span>P<\/span>(<\/span>A<\/span>) <\/span> <\/span>P<\/span>(<\/span>A <\/span>[ <\/span>B<\/span>) <\/span> <\/span>P<\/span>(<\/span>A<\/span>) + <\/span>P<\/span>(<\/span>B<\/span>)<\/span>:<\/span><\/p>\n

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Problem 3. <\/span>A psychologist determined that the number of sessions required to obtain the<\/span><\/p>\n

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trust of a new patient is either 1, 2, or 3. Let <\/span>X <\/span>be a random variable indicating the number<\/span><\/p>\n

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of sessions required to gain the patients’s trust. The following probability distribution has<\/p>\n

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been proposed.<\/p>\n

f<\/span>(<\/span>x<\/span>) =<\/span><\/p>\n

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x<\/p>\n

6<\/p>\n

;<\/p>\n

for <\/span>x <\/span>= 1<\/span>; <\/span>2<\/span>; <\/span>or 3.<\/span><\/p>\n

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a. Write the probability distribution in the form of a table, similar to the ones found on<\/p>\n

Lecture 5. Check if this function <\/span>f <\/span>is indeed a probability distribution.<\/span><\/p>\n

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b. What is the probability that it takes <\/span>exactly <\/span>2 sessions to gain the patient’s trust?<\/span><\/p>\n

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c. What is the probability that it takes <\/span>at least <\/span>2 sessions to gain the patient’s trust?<\/span><\/p>\n

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d. Calculate the expected value <\/span>E<\/span>(<\/span>X<\/span>) and variance <\/span>V ar<\/span>(<\/span>X<\/span>).<\/span><\/p>\n

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e. Suppose we dene a new random variable <\/span>Y <\/span>as<\/span><\/p>\n

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Y <\/span>= 1<\/span>[<\/span><\/span>X<\/span><\/span>=1] <\/span><\/span>=<\/span><\/p>\n

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(<\/p>\n

1<\/span>; <\/span>if <\/span>X <\/span>= 1;<\/span><\/p>\n

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0<\/span>; <\/span>if <\/span>X <\/span>6<\/span>= 1<\/span>:<\/span><\/p>\n

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Write the probability distribution of <\/span>Y <\/span>in the form of a table, and interpret the meaning<\/span><\/p>\n

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of this random variable.<\/p>\n

f. Calculate <\/span>E<\/span>(<\/span>Y <\/span>) and <\/span>V ar<\/span>(<\/span>Y <\/span>).<\/span><\/p>\n

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PSTAT 109: Quiz 3 \u00a0 \u00a0 Winter 2014 Instructions: Please show all work in an organized fashion for full credit. Problem 1. Let = f1; 2; 3g, and consider the family of subsets A of : \u00a0 A = f;;; f1; 2g; f2; 3g; f2g; f1; 3gg: \u00a0 Explain why A is not a sigma-algebra. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[],"class_list":["post-7647","post","type-post","status-publish","format-standard","hentry","category-homework-help"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/7647","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=7647"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/7647\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=7647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=7647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=7647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}