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1. Let X be a random variable with µ = E(X) and σ2 = V (X). Define X∗ = (X -µ)/σ. The random variable X∗ is called the standardized random variable associated with X. Show that this standardized random variable has expected value 0 and variance 1.
2. Peter and Paul play Heads or Tails. Let Wn be Peter's winnings after n matches. Show that E(Wn) = 0 and V (Wn) = n.
3. Find the expected value and the variance for the number of boys and the number of girls in a royal family that has children until there is a boy or until there are three children, whichever comes first.
What are the control limits of the X chart, if α = 0.0026 and the sample size is 4 ?
question an opportunity sample of 50 undergraduate students was asked to complete a series of personality
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The new Twinkle bulb is being developed to last more than 1000 hours. A random sample of 100 of these new bulbs is selected from the production line.
Why is expectation important? Explain what the expected value of an experiment or a business represents. What does it mean to have an expected value of 0? Provide an example of expectation and the use of the formula for expected value.
Can the company conclude that the mean kilo of product treated in one hour by this machine is more than 15,000? Use a 5% level of significance.
which of the following is not an advantage of nonparametric methods over parametric methods?a they can be used when the
There are 72 data values altogether. The degrees of freedom for the Between(dfB) and the degrees of freedom for the With-in (dfW) are?
the diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard
What is the minimal number of days a person must watch to be at least 96.8% sure of seeing one or more hawks migrating?
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