Variance of random

Probability Level 2

A unbiased coin is tossed twice. Let random variable $X$ represents number of tails shown. Find the variance of $X$ .

The answer is 0.5.

1 solution

Thushar Mn
Mar 3, 2016

Xi	P(Xi)
0	.25
1	.25
2	.25

so,

  m1=0 * 0.25 + 1 * 0.25 + 2 * 0.25= 1 

  m2=0(squ) * 0.25 + 1(squ) *  0.25 +2(squ) *  0.25    =1.5

  variance = m2 - m1(squ) =1.5 - 1 =0.5

I think something's off in your chart + explanation. Although the answer is the same. For one thing, the sum of $P(X_i)$ must $= 1$ .
|| $X_i$ || $P(X_i)$ ||
||0||0.25||
||1||0.5||
||2||0.25||

So $m_1 = (0 \times 0.25) + (1 \times 0.5) + (2 \times 0.25) = 1$ $m_2 = (0^2 \times 0.25) + (1^2 \times 0.5) + (2^2 \times 0.25) = 1.5$
variance $= m_2 - m_1^2 = 1.5 - 1.0 = 0.5$

Christopher Williams - 4 years, 9 months ago

the above math given by the solution is wrong

m1=0 * 0.25 + 1 * 0.25 + 2 * 0.25= 1

Also the probability of having 1 tail is not 0.25

The comment however corrected it.

Xun Ding - 3 years, 3 months ago

Variance of random

The answer is 0.5.

1 solution

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