Question

The probability that x falls between two values, say a and b, is the same as...

The probability that x falls between two values, say a and b, is the same as the probability that x falls between two other values, say c and d. The interval between a and b is the same size as the interval between c and d (i.e., b–a = d–c). Based on this information, can it be concluded that the variable x is uniformly distributed? Explain. Your explanation must be supported by graphical evidence.

Math   Statistics-And-Probability   
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Answer #1

We know from the question that.

P(a<X<b)=P(c<X<d) and d-c=b-a ; i.e.the size of the interval (a,b) and (c,d) is same.

This implies that a randomly chosen point falling in two arbitrary intervals of same length have equal probability which is the base of uniform distribution. That is in uniform distribution, each interval of same length has equal probability of getting x.

So the information given in the question is enough to conclude that the random variable x is uniformly distributed.

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