Given the joint density function below, find P(2
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- 4. Suppose that the joint distribution of X and Y can be modeled by the following probability density function: S(x, y) = 6x³y, [0, 0Find c that will make the following a valid density function:Given fty)=ky, 2sy <8, and fly)=0 clsewhere. a. Find the value of k for which fy) is a valid density function? b. Find P(1Given the joint density functiona. Verify that the function is a joint density functionb. Find P(1<Y<3|X=1)The density function of a 1 meter long fishing rod is d(x)= 100 grams per meter, where x is the 1+x? distance from the handle in meters. a. Find the total mass of this fishing rod. b. Find the center of mass of this fishing rod.Step 3: Expression for density function of T, in the convolution, isn't (t-s1) term extra?Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,