only que no. 4 nours 4. Let X be the random variable whose probability density function is

only que no. 4

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nours 4. Let X be the random variable whose probability density function is Sce-5z, if z>0 се f(r) = 10, if otherwise (a) Find c. (b) Find P(1 <2X - 1<9). (c) Find F(2) where F denotes the c.d.f. of X. (d) Write an equation to find E[3X2 + 15]. You do not have to evaluate it. 5. Let a <b be real numbers. Let X be a random variable such that it is known that a SXS6 and for every subinterval of (a, b), the probability that X will belong to that subinterval is proportional to the length of that subinterval. Then we say X has the uniform distribution on the interval (a, b and the probability density function of X is given by if a sasb otherwise f(r) = and we write X~U(a, b) nours 4. Let X be the random variable whose probability density function is Sce-5z, if z>0 се f(r) = 10, if otherwise (a) Find c. (b) Find P(1 <2X - 1<9). (c) Find F(2) where F denotes the c.d.f. of X. (d) Write an equation to find E[3X2 + 15]. You do not have to evaluate it. 5. Let a <b be real numbers. Let X be a random variable such that it is known that a SXS6 and for every subinterval of (a, b), the probability that X will belong to that subinterval is proportional to the length of that subinterval. Then we say X has the uniform distribution on the interval (a, b and the probability density function of X is given by if a sasb otherwise f(r) = and we write X~U(a, b)