document.write( "Question 1190605: The probability distribution of a discrete random variable X is given below.\r
\n" ); document.write( "\n" ); document.write( "Value x of X: \"-2, -1, 0, 1, 2\"
\n" ); document.write( "P(X=x): \"0.22, 0.11, 0.26, 0.12, 0.29\"\r
\n" ); document.write( "\n" ); document.write( "Let F(x) be the cumulative distribution function of X. Compute the following:\r
\n" ); document.write( "\n" ); document.write( "a) F(x=1)=
\n" ); document.write( "b) F(x=1)-F(x=-1)=
\n" ); document.write( "c) F(x=3/5)=\r
\n" ); document.write( "\n" ); document.write( "Any help would be appreciated, thank you! \n" ); document.write( "

Algebra.Com's Answer #822326 by chitrank(4) $\"\"$ $\"About$

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Cumulative distribution function(CDF) is nothing but a function that tells you, given some number x, what is the probability that the random variable $\"X\"$ would be less than or equal to that value $\"x\"$ .\r
\n" ); document.write( "\n" ); document.write( "So to calculate CDF on x, or f(x) as in the question, just find out what's the probability that the random variable $\"X\"$ will take a value less than or equal to $\"x\"$ . \r
\n" ); document.write( "\n" ); document.write( "To calculate that probability, observe that $\"X\"$ can only take one value at any given time. Therefore, to calculate the probability that $\"X\"$ would be less than (or equal to) some $\"x\"$ , you would only need to sum the probabilities of $\"X\"$ taking values than or equal to $\"x\"$ . And this sum is extremely easy because $\"X\"$ is discrete, and hence $\"X\"$ only takes finitely many values (which is, according to the question, one of -2,-1,0,1,2).\r
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