Answer to Question #304895 in Statistics and Probability for ced

Question #304895

Below is an incomplete probability distribution for a random variable X.




x 1 2 3 4 5 6



f(x) 0.15 0.25 0.33 0.09




(a) If f(4) = P(X = 4) = 2P(X = 5), complete the probability distribution above.



(b)Construct a probability histogram of this distribution.



(c) Find the cumulative distribution of the random variable X.



(d)Construct a graph of the cumulative distribution.

1
Expert's answer
2022-03-07T06:34:04-0500

(a)


"0.15 +0.25+ 0.33+ 0.09+k=1"

"k=1-0.82=0.18"

"P(X=5)=\\dfrac{1}{2}P(X=4)=\\dfrac{1}{2}(0.09)=0.045"

"P(X=6)=k-P(X=5)=0.18-0.045=0.135"

"\\def\\arraystretch{1.5}\n \\begin{array}{c:c}\n x & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline\n f(x) & 0.15 & 0.25 & 0.33 & 0.09 & 0.045 & 0.135\n\\end{array}"

(b)




(c)


"F(x) = \\begin{cases}\n 0 &x<1 \\\\\n 0.15 &1\\le x<2\\\\\n 0.40 &2\\le x<3\\\\\n 0.73 & 3\\le x<4\\\\\n 0.82 & 4\\le x<5\\\\\n 0.865 & 5\\le x<6\\\\\n 1 & x\\ge6\\\\\n\\end{cases}"

(d)


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