The Probability Distributions with Different Sample Sizes a. Let X has three possible outcomes, )(=x0=1)__t X=x1=1 , X=x2=2. The probability of each outcome is: PX=x0=0.L PX=x0=0.5 , PX=x0=0.3. Run a simple random sampling by picking two outcomes consecutively and independently from X (this is the sampling method so called sampling with replacement). Answer the following questions: (Hintl: sample size n = 2) ((Hint2: construct a table for possible outcomes and the probability of possible outcomes.) Construct the distribution table for sample mean X and sample variance 52. b. Is the center of sample distribution same as the population? Is the center of sample variance E52 same as the Spread of population 2? Explain your answers. c. When sample size is increased to 49, i.e., picking 49 outcomes with replacement, what is the probability that the sample mean is greater than 0.8 but Smaller than 1.2