Distribution and probabilities for basketball game Shortly the task says, that we have two basketball teams. Predictably first team will win by $3.5$ points. Also, with probability $p_1=0.5$, first team will win by $4,5,6,7,\ldots$ points (mark $-4,-5,-6,\ldots$) or with probability $p_2=1-p_1=0.5$ first will win by $3,2,1$ points OR lose with any result ($-3,-2,-1,0,1,2,\ldots$). 


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*With which distribution can we calculate the probabilities that first team will win by any number of points ($\ldots,2,1,0,-1,-2,-3,\dots$)? 

*Calculate probability that the difference of points between two teams will be in interval  $[6,10]$.


I'm new in MSE and in this field/ Really need help with this task or some hints. Is it enough data to calculate these things?
 A: This is a poorly posed question.  Certainly it is impossible that the first team will win by $3.5$ points.  It could be that the mean score difference is $3.5$.  That gives you one constraint on the distribution function of the score difference.  For point $1$ what distribution is the question referring to?  If it is the distribution of the score difference, we can use any distribution to compute the probability.  Just look at the value of the distribution at that point differential.  For point $2$ it depends on the distribution.  One distribution that satisfies the requirement is that the point differential is either $3$ or $4$ with each having probability $0.5$.  The chance the difference is in $[6,10]$ is then zero.  Another is that the differential is either $8$ or $-1$ with each having probability $0.5$.  Then the chance the difference is in $[6,10]$ is $0.5$.  There are an infinite number of other distributions with other chances that the difference is in $[6,10]$
A: You should try a normal Distribution with continuity correction, and make some assumptions on the standard deviation.
