1 answer

IS 3x+1 # 6 Given that f(x) = is a probability distribution for a random variable...

Question:

IS 3x+1 # 6 Given that f(x) = is a probability distribution for a random variable that can take on the values x = 1,2,3,4,5,
IS 3x+1 # 6 Given that f(x) = is a probability distribution for a random variable that can take on the values x = 1,2,3,4,5, find an expression for the cumulative distribution function F(x) of the random variable. 50

Answers

Here,

f(0) = 3.7 +1 50

x= 1,2,3,4,5

Here F(X) is the cumulative distribution function i.e.F(X) = P(X <I)

The following table shows the calculation for CDF.

X P(X=x) F(X)
1

4 3*1+1 50 50

50
2

\frac{3*2+1}{50}=\frac{7}{50}

\frac{4}{50}+\frac{7}{50}=\frac{11}{50}
3 10 3+3+1 50 50

\frac{4}{50}+\frac{7}{50}+\frac{10}{50}=\frac{21}{50}

4

3+4+1 13 50 50 \frac{4}{50}+\frac{7}{50}+\frac{10}{50}+\frac{13}{50}=\frac{34}{50}

5

3+5+1 16 50 50 \frac{4}{50}+\frac{7}{50}+\frac{10}{50}+\frac{13}{50}+\frac{16}{50}=\frac{50}{50}=1
X 1 2 3 4

5

P(X=x) \frac{2}{25} \frac{7}{50} \frac{1}{5} \frac{13}{50}

\frac{8}{25}

F(X)=P(X\leq x) \frac{2}{25} \frac{11}{50} \frac{21}{50} \frac{17}{25}

1

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