anonymous
  • anonymous
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.
Mathematics
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SOLVED
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chestercat
  • chestercat
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amoodarya
  • amoodarya
|dw:1434986852277:dw| this is first step
anonymous
  • anonymous
yes then... atleast someone to help me..
amoodarya
  • amoodarya
\[e(x)=\sum_{i=1}^{5}p_ix_i\]

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amoodarya
  • amoodarya
\[e(x)=\frac{1}{32}*0+\frac{5}{32}*1+\frac{10}{32}*2+\frac{10}{32}*3+\frac{5}{32}*4+\frac{1}{32}*5\]
amoodarya
  • amoodarya
it is ok , to calculate mean ?
anonymous
  • anonymous
yes thank you so much...
amoodarya
  • amoodarya
\[var(x)=e[x^2]-e^2[x]\\and\\e[x^2]=\sum_{i=1}^{5}p_ix_i^2\]
amoodarya
  • amoodarya
can you tell me what;s mean ? then what is the value of var (x) ?
anonymous
  • anonymous
mean is 2.5 var(x)=1.25 right ?
amoodarya
  • amoodarya
can I see your work ?
amoodarya
  • amoodarya
\[mean=\frac{80}{32} ?\]
anonymous
  • anonymous
yes its 80/32
amoodarya
  • amoodarya
yes it is correct
amoodarya
  • 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

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