Suppose a value z of the continuous random variable Z is generated as follows: First, a fair die is rolled.If the side of the die facing up has 1 or 2 dots, then z is drawn from a Unif(0,2) distribution;otherwise z is drawn from a Unif(1,4) distribution. Now for such random variable Z how can you find a P(1<Z<2)?? I am just unable to comprehend what the Z random variable would even look like.
2026-04-05 20:15:22.1775420122
How do I find $P(1< Z <2)$ for given problem?
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There's a 1/3 chance the die rolls 1 or 2 dots (called "pips," incidentally), and then a 1/2 chance the variable is between $1$ and $2$.
There's a 2/3 chance the die rolls 3, 4, 5 or 6 pips, and then a $1/3$ chance the variable is between $1$ and $2$.
So....