Computer Science Data Sci questions. Sorry that there are many small questions but please help me as many as you can. I will appreciate. I will give an upvote.

No need to type in Latex format, just regular work, thank you!

Suppose you are modeling the probability of observing flood levels of various heights when there is a storm in a particular coastal city. Let X be a random variable representing the observed flood height (in feet), which must be nonnegative. There are many different choices for probability density function (pdf) for X. You decide to use the following pdf for X: 0 otherwise where c is some normalizing constant. Part A: Determine the value of c such that fCx) is a valid density function Type Markdown and LaTeX: Part B: Compute the cumulative density (cdf) function F(x) for X. Then, conduct two sanity checks: First, what should F(0) equal? Second, what should be the limit of F(x) as x oo? Be sure to justify these answers. Verify that F(0) and lim F(x) satisfy your hypotheses using cdf you derived. Type Markdown and LaTeX: r Part C: Use the cdf you derived in Part B to calculate the median, E, of the probability density for X. Suppose you are modeling the probability of observing flood levels of various heights when there is a storm in a particular coastal city. Let X be a random variable representing the observed flood height (in feet), which must be nonnegative. There are many different choices for probability density function (pdf) for X. You decide to use the following pdf for X: 0 otherwise where c is some normalizing constant. Part A: Determine the value of c such that fCx) is a valid density function Type Markdown and LaTeX: Part B: Compute the cumulative density (cdf) function F(x) for X. Then, conduct two sanity checks: First, what should F(0) equal? Second, what should be the limit of F(x) as x oo? Be sure to justify these answers. Verify that F(0) and lim F(x) satisfy your hypotheses using cdf you derived. Type Markdown and LaTeX: r Part C: Use the cdf you derived in Part B to calculate the median, E, of the probability density for X