The continuous random variable T represents the time in hours that students spend on homework. The cumulative distribution function of T is given by: t< 0, F(t) = 0sts 1.5, t> 1.5. Then P(2T > 1)= 8/9 513/625 None of these O 11/16
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- Suppose the lengths of human pregnancies are normally distributed with u = 266 days and 0 = 16 days. The area to the left of X = 245 is 0.0947. What is the probability that a randomly selected human pregnancy lastsThe joint distribution of the pair of random variables as given in the following table: 0 Y 1 2 -10 X 0 10 0.2 0.1 0 0.066 0.046 0.052 0.072 0.042 O No answer 0.1 0.2 0 0.1 0.1 0.2 A random sample of 4 is taken of the random variable X. What is pZX₁/425? (EX//425) ²ty
- Suppose we have a continuous random variable over -2Find the first two moments about the mean for the random variable X defined by X = -2 with prob. 1/3 3 with prob. 1/2 = 1 with prob. 1/6. %3DIf the random variable X as a mean of u and a variance of o2 what is the P((X-u)² < 20): O less that equal to 1/4 O greater than or equal to 3/4 cannot tell O equal to 5/4Suppose that X₁,..., Xn are i.i.d. from a normal population with mean μ and variance o². Calculate the expected value and the variance of the sample mean X and find the distribution of √n(X − µ).The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)Clear my choice on 3 Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)=D0.5, P(2)=0.2 and P(3)=D0.3 then P(X>1) is equal to: et answered ed out of 1.00 Select one: g question O a. 0.3 Ob. 0.2 Oc. 0.5 d. 0 Next pagThe Volatility X for the S&P stock index on a given day is a normal random variable with mean = 10 and standard deviation = 2 The volatilities recorded over a 100-day period on the S&P500 are Y1, Y2, ... Y100. Assume that these Yi's are independent and identically distributed, uniform on the interval [5,15]. Let V = (Y1 + Y2 + ... + Y100)/100. What approximately is P[9.5 < V < 10.5]?find oc x is a a normal mean U=3 805-0-5 random distribution P (ocLet L be the random variable for the length of time, in years, that a person will remember an actuarial statistic. For a certain popula- tion, L is exponentially distributed with mean 1/Y, where Y has a gamma distribution with a = 4.5 and 3 = 4. Find the variance of L.SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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