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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.A random variable X undergoes the transfor- a mation Y= where 'a' is the real number. Find the density function of Y.Two han dom. variables, X and Y, have a joint probability density function given by DEXZT 2 ण्डपड़ा f(x, y) = elsewhere setermine the value of k that makes valid probability density function. this a Skxy to Determine the joint probability distribu- tion function F(x, y) Find event the joint probability of the xºs ₂2 and y² = /2
- If foxy)=k(y-2x) is a joint density function over Ox², then what is the value of the constant k? Provide a numerical answer only4. Suppose that the joint distribution of X and Y can be modeled by the following probability density function: S(x, y) = 6x³y, [0, 0Let X and Y have the following joint density function: for 0Derive the density function of Y=eZ , where Z ∼ N(μ,σ2) . This is called the lognormal density. Do not just state the lognormal density. Show how you can derive it from a certain density.If the RV X follows N(0, o), find the density function of Y = aX², using the characteristic function technique. %|If X and Y are independent RVs with pdf's e*, x20, and e, y 2 0, respectively, find the density functions of U = X and V=X+Y. Are U and V independent? %3D X + YRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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