Suppose the body length of a certain species is normally distributed with mean 39.8 in and standard deviation 2.05 inches. What is the probability that a randomly selected member of this species will have a body length of at least 40 inches? Suppose that every three months, on average, an earthquake occurs in a certain region. Assuming this is a Poisson process, what is the probability that the next earthquake occurs after three but before seven months? Suppose that, on average, y-particles emitted from a substance follow a Poisson process. Suppose moreover that four particles are emitted every second. What is the probability that will take at least 2 seconds before the next two y-particles are emitted? The proportion of stocks that will increase in value is a beta random variable with a = 4 and ,8 = 3. What is the probability that at least 70% of the stocks will increase in value? Letf(x,y) = A(x2/3 +y2/3) inO S x S 1 and 0 S y S 2. (3) Determine the value ofthe constant A that makes f(x, y) a joint probability density function. (b) Compute P (X S ,Y 2 2)