Chapter: Probability Distributions· Mathematics & Statistics (Commerce) Part 2
The probability distribution of \(X\) is as follows:\(x\)01234\(P[X=x]\)0.1\(k\)\(2k\)\(2k\)\(k\)Find (a) \(k\) (b) \(P(X\gt 2)\) (c) \(P(1\lt X\le 4)\)Solution:The table gives a probability distribution and therefore\(\Sigma P(X=x)=1\)\(P(X=0)+P(X=1…
Q.6 (C) (ii) The probability distribution of \(X\) is as follows:
| \(x\) | 0 | 1 | 2 | 3 | 4 |
| \(P[X=x]\) | 0.1 | \(k\) | \(2k\) | \(2k\) | \(k\) |
Find (a) \(k\) (b) \(P(X\gt 2)\) (c) \(P(1\lt X\le 4)\)
Solution:
The table gives a probability distribution and therefore
\(\Sigma P(X=x)=1\)
\(P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=1\)
\(0.1+k+2k+2k+k=1\)
\(6k=1-0.1\)
\(6k=0.9\)
\(k=\)[ ]
\(P(X\gt 2)=P(X=3)+P(X=4)\)
\(=2k+k\)
\(=\)[ ]
\(P(1\lt X\le 4)=P(X=\)[ ]\()+P(X=3)+P(X=4)\)
\(=\)[ ]\(+2k+k\)
\(=0.75\)