Let $X$ and $Y$ be continuous random variables with probability density functions $P_X(x)$ and $P_Y(y)$, respectively. Further, let $Y=X^2$ and $P_X(x)=\left\{\begin{array}{cc}1, & x \in(0,1] \\ 0, & \text { otherwise }\end{array}\right.$.

The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________ (Round off to 3 decimal places).

Let the probability density function of a random variable x be given as

f(x) = ae^$$-$$2|x|

The value of a is _________.

Suppose the probability that a coin toss shows "head" is $p$, where $0 < p < 1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is :