Problem set for binomial probability distribution 1.)Use the formula for

Joni Kenny 2021-10-01 Answered
Problem set for binomial probability distribution
1.)Use the formula for the binomial probability distribution to find the probabilities for \(\displaystyle{n}={4}.{p}={0.5}\) and \(\displaystyle{x}={0}.{1}.{2}.{3}\). and 4.

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Expert Answer

crocolylec
Answered 2021-10-02 Author has 18756 answers

Step 1
Given data:
\(\displaystyle{n}={4},{p}={0},{5}\) and \(\displaystyle{x}={0},{1},{2},{3},{4}\)
\(\displaystyle{q}={1}-{p}\)
\(\displaystyle={1}-{0},{5}\)
\(\displaystyle={0},{5}\)
Binomial Probability distribution:
\(P(X=n)=\sum_{x=0}^{n} \left(\begin{array}{c}n\\ x\end{array}\right)p^{x}q^{n-x}\)
\(\displaystyle{P}{\left({X}-{4}\right)}={P}{\left({0}\right)}+{P}{\left({1}\right)}+{P}{\left({2}\right)}+{P}{\left({3}\right)}+{P}{\left({4}\right)}\)
\(=\left(\begin{array}{c}4\\ 0\end{array}\right)\left(0,5\right)^4\left(0,5\right)^\left\{4-0\right\}+\left(\begin{array}{c}4\\ 1\end{array}\right)\left(0,5\right)^4\left(0,5\right)^\left\{4-1\right\}+\left(\begin{array}{c}4\\ 2\end{array}\right)\left(0,5\right)^4\left(0,5\right)^\left\{4-2\right\}+\left(\begin{array}{c}4\\ 3\end{array}\right)\left(0,5\right)^4\left(0,5\right)^\left\{4-3\right\}+\left(\begin{array}{c}4\\ 4\end{array}\right)\left(0,5\right)^4\left(0,5\right)^\left\{4-4\right\}\)
\(\displaystyle{P}{\left({X}={4}\right)}={0.0039}+{0.03125}+{0.09375}+{0.125}+{0.0625}={0.3164}\)
Conclusion
Hense, the binomial probability distribution of \(\displaystyle{P}{\left({X}={4}\right)}={0.03164}\)

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