## anonymous one year ago helllllllllllllllp please.. medal and fans A fair coin is tossed 5 times and the number of heads is recorded. (i) The random variable X is the number of heads. State the mean and the variance. (ii) The number of heads is doubled and denoted by the random variable Y. State the mean and variance of Y.

1. amoodarya

|dw:1434986852277:dw| this is first step

2. anonymous

yes then... atleast someone to help me..

3. amoodarya

$e(x)=\sum_{i=1}^{5}p_ix_i$

4. amoodarya

$e(x)=\frac{1}{32}*0+\frac{5}{32}*1+\frac{10}{32}*2+\frac{10}{32}*3+\frac{5}{32}*4+\frac{1}{32}*5$

5. amoodarya

it is ok , to calculate mean ?

6. anonymous

yes thank you so much...

7. amoodarya

$var(x)=e[x^2]-e^2[x]\\and\\e[x^2]=\sum_{i=1}^{5}p_ix_i^2$

8. amoodarya

can you tell me what;s mean ? then what is the value of var (x) ?

9. anonymous

mean is 2.5 var(x)=1.25 right ?

10. amoodarya

can I see your work ?

11. amoodarya

$mean=\frac{80}{32} ?$

12. anonymous

yes its 80/32

13. amoodarya

yes it is correct

14. amoodarya

if you want to know more in binomial distribution mean=np=5 (1/2)=2.5 var=n p q =5 (1/2)(1/2)=5/4=1.25