Q3: Errors in an experimental transmission channel are found when the transmission is checked by a certifier that detects missing pulses. The number of errors found in an eight-bit byte is a random variable with the following distribution: x<1 0.7 1sx<4 F(x)=- 0.9 4sx<7 1 (a) P(X<4) (b) P(X>7) c) P(X<5)
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- Q.7: Three dice are rolled and their results are added up. (1) What is the size of the sample space for this experiment? (1I) What is the potential candidate to define for a random variable? (III) What is the probability of the values of the values of the random variable you have defined in (II) above lying in the range [5, –7]?28 - The variance of the sample formed by the sample averages of the samples randomly taken from a population with a size of n=7 with the condition of substitution was found to be 0.68. What is the sample standard error value? a) 0.31 B) 0.05 NS) 0.26 D) 0.82 TO) 0.34Find the following probabilities for the standard normal random variable z (1 point) Find the following probabilities for the standard normal random variable z: (a) P(-2.17 -0.56) =
- 9) We assume that X is a random variable with the values 2: 4; 6; 8 and that the distribution isp (2) = p (4) = p (6) = p (8) = 1/4. Then the variance of X isa) 3b) 7c) 4d) none of theseIf the random variable X is normal with mean 2 and standard deviation 2, then what is P(x2 - 4x < 1). 3Show that the Pareto does not have finite mean or variance by calculating the mean and variance of a strict Pareto random variable. Are there any values of α for which either does not take a finite value? [HINT: Examine the case when α ∈ (0, 1] and α > 1]
- If x is a binomial random variable, compute the mean, the standard deviation o, and the variance 2 for each of the following cases: (a) n = = 6, p = 0.1 fl = 0²: % σ= = (b) n = 5, p = 0.2 fl = 0². σ= (c) n = 3, p = 0.8 fl = 0²: 0 = 0² || (d) n = 5, p = 0.6 fl = % 0 =Let X be a normal random variable with = 10 and = 2. Find the values of P(X < 11) b. P(X > 8) P(7 < X < 9)Consider a random variable X that is equal to the sum of the outcomes of a 4-sided dice throw anda 6-sided dice throw. [Note: this same experiment will be used in the first four questions of the assignment.) Calculate: What is the variance of X? [Use 2 decimals if your answer is not an integer.)
- Example 2.14. Show the CDF of the random variable X with the following pdf: Sx(2) = lwa(x) Example 2.15. Let X be a random variable with the following pdf: 1. Find its CDF. 2. Evaluate the following probabilities using its CDF and/or pdf. a) P(} 1) c) P(X > }|X < 1)Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LOA European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 325 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.5% and standard deviation σ = 0.9%.A button hyperlink to the SALT program that reads: Use SALT.(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 325 stocks in the fund) has a distribution that is approximately normal? Explain. Yes, x is a mean of a sample of n = 325 stocks. By the central limit theorem, the x distribution is approximately normal. (b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.) (c) After 18 months, what is the probability that the average monthly…