Suppose the cumulative distribution of random variable X is F(x) 0 x&lt; 0 0.2 x 0 &lt;= x &lt; 5 1 5 &lt;=x Determine the following: (a) P (X &lt; 2.8) (b) P (X &gt; 1.5) (c) P (X &lt; -2) (d) P (X &gt; 6)

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Suppose the cumulative distribution of random variable X is F(x) 0 x&amp;lt; 0 0.2 x 0 &amp;lt;= x &amp;lt; 5 1 5 &amp;lt;=x Determine the following: (a) P (X &amp;lt; 2.8) (b) P (X &amp;gt; 1.5) (c) P (X &amp;lt; -2) (d) P (X &amp;gt; 6)

Jazz Frenia · Accepted Answer

To solve the given problem, let&#039;s evaluate the probabilities for each case:(a) P(X &amp;lt; 2.8)Since 0 &amp;lt;= x &amp;lt; 5, we can calculate the probability as the difference between the cumulative distribution at 2.8 and the cumulative distribution at 0:P(X &amp;lt; 2.8) = F(2.8) - F(0) = 0.2 - 0 = 0.2(b) P(X &amp;gt; 1.5)Since 0 &amp;lt;= x &amp;lt; 5, we can calculate the probability as the difference between 1 and the cumulative distribution at 1.5:P(X &amp;gt; 1.5) = 1 - F(1.5) = 1 - 0.2 = 0.8(c) P(X &amp;lt; -2)Since x &amp;lt; 0 for all values, the probability of X being less than -2 is 0:P(X &amp;lt; -2) = 0(d) P(X &amp;gt; 6)Since 5 &amp;lt;= x for all values, the probability of X being greater than 6 is 0:P(X &amp;gt; 6) = 0Therefore, the probabilities are:(a) P(X &amp;lt; 2.8) = 0.2(b) P(X &amp;gt; 1.5) = 0.8(c) P(X &amp;lt; -2) = 0(d) P(X &amp;gt; 6) = 0

Suppose the cumulative distribution of random variable X

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