If a random variable $X$ has the following probability distribution values
Then $P(X \geq 6)$ has the value

Question

If a random variable $X$ has the following probability distribution values Then $P(X \geq 6)$ has the value

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Since } \sum_{x=0}^7 \mathrm{P}(\mathrm{X}=x)=1 \ & \begin{array}{l}0+\mathrm{k}+2 \mathrm{k}+2 \mathrm{k}+3 \mathrm{k}+\mathrm{k}^2+2 \mathrm{k}^2+7 \mathrm{k}^2+\mathrm{k}=1 \ \begin{aligned} & \Rightarrow 10 \mathrm{k}^2+9 \mathrm{k}-1=0 \ & \Rightarrow(\mathrm{k}+1)(10 \mathrm{k}-1)=0 \ & \Rightarrow \mathrm{k}=\frac{1}{10}\end{aligned} \ \begin{aligned} \mathrm{P}(\mathrm{X} \geq 6) & =\mathrm{P}(\mathrm{X}=6)+\mathrm{P}(\mathrm{X}=7) \ & =2\left(\frac{1}{10}ight)^2+7\left(\frac{1}{10}ight)^2+\frac{1}{10} \ & =\frac{2}{100}+\frac{7}{100}+\frac{10}{100} \ & =\frac{19}{100}\end{aligned}\end{array} \begin{array}{l}	ext {. }\end{array}\end{aligned}$ $\ldots[\because \mathrm{k} \geq 0]$

If a random variable $X$ has the following probability distribution values Then $P(X \geq 6)$ has the value

Solution