JEE Main 2005 — Probability & Statistics

Let $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{\mathrm{n}}$ be $\mathrm{n}$ observations such that $\sum \mathrm{x}_{\mathrm{i}}^2=400$ and $\sum \mathrm{x}_{\mathrm{i}}=80$. Then a possible value of $\mathrm{n}$ among the following is

A random variable $X$ has Poisson distribution with mean 2. Then $P(X>1.5)$ equals

Let $A$ and $B$ be two events such that $P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{1}{4}$, where $\bar{A}$ stands for complement of event $A$. Then events $A$ and $B$ are

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately