Please answer b **Problem Statement:**Each rear tire on an experimental airplane is supposed to be filled to a pressure of 47 pounds per square inch (psi). Let $ X $ denote the actual air pressure for the right tire and $ Y $ denote the actual air pressure for the left tire. Suppose that $ X $ and $ Y $ are random variables with the joint density function shown below. Complete parts (a) through (c).**Joint Density Function:**\[f(x, y) = \begin{cases} k(x^2 + y^2), & 33 \leq x < 61, \ 33 \leq y < 61 \\0, & \text{elsewhere}\end{cases}\]---**Problem Parts:**(a) **Find $ k $:**\[k = \frac{3}{10698464}\](b) **Find $ P(33 \leq X \leq 44 \ \text{and} \ 51 \leq Y \leq 61) $:**\[P(33 \leq X \leq 44 \ \text{and} \ 51 \leq Y \leq 61) = \boxed{\quad}\](Simplify your answer.) ---**Notes:**To solve this problem, you would need to integrate the joint density function over the specified intervals for $ X $ and $ Y $, using the constant $ k $ found in part (a).

Let X denote the actual air pressure for the right tire. and Y denote the actual air pressure for the left tire. Suppose the joint density function of random variable X and Y is given below: fx,y=kx2+y2 ; 33≤x≤61, 33≤y≤61 0 ; elsewhere Also given that, K= 310698464 Therefore the given joint pdf is can be written as: fx,y=310698464x2+y2 ; 33≤x≤61, 33≤y≤61 0 ; elsewhereb. P33≤X≤44 and 51≤Y≤61=∫3344 ∫5161f(x,y)dydx=∫3344 ∫5161310698464x2+y2 dydx=310698464∫3344 ∫5161x2+y2 dydx=310698464∫3344 x2y+y335161dx=310698464∫3344 x2×61+6133-x2×51+5133dx=310698464∫3344 10x2+943303dx=31069846410x33+943303x3344=31069846410×4433+943303×44-10×3333+943303×33=31069846450023603-34722603=153010010698464=0.143021P33≤X≤44 and 51≤Y≤61≅0.1430