an unbiased coin is tossed three times if a discrere random variable X denoted the number of times a tail appears 1. list the sample space 2. find the distribution of X 3. the mean of X


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 123389 by aurpeyz last updated on 25/Nov/20

$a n u n b i a s e d c o i n i s t o s s e d t h r e e t i m e s i f a d i s c r e r e$ $r a n d o m v a r i a b l e X d e n o t e d t h e$ $n u m b e r o f t i m e s a t a i l a p p e a r s$ $1 . l i s t t h e s a m p l e s p a c e$ $2 . f i n d t h e d i s t r i b u t i o n o f X$ $3 . t h e m e a n o f X$
	Answered by som(math1967) last updated on 25/Nov/20
	$1.(TTT ,TTH ,THT, HTT, THH HHT, HTH ,HHH) probability of tail=p=(1/2) probability of head=q=(1/2) P(X)=^n c_r p^r q^(n−r) i{No tail . P(X=0)=^3 c_0 ((1/2))^0 ((1/2))^(3−0) =(1/8) ii)one tail P(X=1)=^3 c_1 ((1/2))^1 ((1/2))^(3−1) =(3/8) iii)2 tail =(3/8) iv)3 tail =(1/8) 2. { (x,0,1,2,3),((P(x)),(1/8),((3 )/8),(3/8),(1/8)) :} 3. Mean x^− =0×(1/8)+1×(3/8)+2×(3/8) 3×(1/8) =((12)/8)=1.5$
	$1 . (TTT, TTH, THT, HTT, THH$ $HHT, HTH, HHH)$ $probability of tail = p = \frac{1}{2}$ $probability of head = q = \frac{1}{2}$ $P (X) =^{n} c_{r} p^{r} q^{n - r}$ $i {No tail .$ $P (X = 0) =^{3} c_{0} {(\frac{1}{2})}^{0} {(\frac{1}{2})}^{3 - 0} = \frac{1}{8}$ $ii) one tail$ $P (X = 1) =^{3} c_{1} {(\frac{1}{2})}^{1} {(\frac{1}{2})}^{3 - 1} = \frac{3}{8}$ $iii) 2 tail = \frac{3}{8}$ $iv) 3 tail = \frac{1}{8}$ $2 . {\begin{cases} x & 0 & 1 & 2 & 3 \\ P (x) & \frac{1}{8} & \frac{3}{8} & \frac{3}{8} & \frac{1}{8} \end{cases}$ $3 . Mean \bar{x} = 0 \times \frac{1}{8} + 1 \times \frac{3}{8} + 2 \times \frac{3}{8}$ $3 \times \frac{1}{8} = \frac{12}{8} = 1.5$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum