iid 2 1. Consider a 3 year investment with annual effective rates 11, 12, 13 in...

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iid 2 1. Consider a 3 year investment with annual effective rates 11, 12, 13 in each year respectively. Assume that the rates are independent and identically distributed, and that (1+1) In N(μ, o²), for some parameters μ E R and σ > 0. Assume further that the initial value of your investment is £100. Let S3 denote the value of the investment at the end of year 3. Finally, assume that E[i] = 0.02 and Var[i1] = 0.01. (b) (c) (d) (e) 2 Prove that S3 ~ N(In 100 + 3μ, 302). S3 = 100. (Hi) (Hin) (mis)_ Calculate and o². e Calculate the expectation and the variance of S3. Els₁) = /00x/02 Calculate the probability P(S3 110). /001.27/10 P(S11 /+R > 1.1 Ray Suppose that 4 is a random variable independent of (11, 12, 13), and assume that 4 has a density function given by 100 100- f(x) = e-1 = for x = [0, 0.01] for x [0, 0.01]. Suppose that you invest the amount S3 for an extra year, this time with annual effective rate 4, and let us denote by S4 the amount of your investment at the end of year 4. Calculate the expectation of S4. iid 2 1. Consider a 3 year investment with annual effective rates 11, 12, 13 in each year respectively. Assume that the rates are independent and identically distributed, and that (1+1) In N(μ, o²), for some parameters μ E R and σ > 0. Assume further that the initial value of your investment is £100. Let S3 denote the value of the investment at the end of year 3. Finally, assume that E[i] = 0.02 and Var[i1] = 0.01. (b) (c) (d) (e) 2 Prove that S3 ~ N(In 100 + 3μ, 302). S3 = 100. (Hi) (Hin) (mis)_ Calculate and o². e Calculate the expectation and the variance of S3. Els₁) = /00x/02 Calculate the probability P(S3 110). /001.27/10 P(S11 /+R > 1.1 Ray Suppose that 4 is a random variable independent of (11, 12, 13), and assume that 4 has a density function given by 100 100- f(x) = e-1 = for x = [0, 0.01] for x [0, 0.01]. Suppose that you invest the amount S3 for an extra year, this time with annual effective rate 4, and let us denote by S4 the amount of your investment at the end of year 4. Calculate the expectation of S4.

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a To prove that S3 follows a lognormal distribution with parameters ln100 3 and 32 we need to show that the logarithm of S3 is normally distributed Le... View the full answer