##Chi-squared distribution##

The chi-squared distribution plays an important role in testing hypotheses about frequencies. To define it, let ${Z_1,Z_2,...,Z_m}$ be independent and standard normally distributed random variables. Then the sum of squares

$$\chi_m^2=Z_1^2+Z_2^2+...+Z_m^2=\Sigma_{i=1}^m Z_i^2$$.

###Example 1###

To view various members of the $\chi^2$ distribution load the `TeachingDemos` package. Use the command `vis.gamma()` to open an interactive display of various distributions. Click on "Visualizing the gamma", "Visualizing the Chi-squared", and adapt "Xmax". Move the "Shape" button to the right to increase the degrees of freedom. Observe that the graphs of chi-squared densities change from heavily skew to the right into more bell- shaped normal as the degrees of freedom increases.

using the above example I need help with writing a code on R and R studio to solve the following question

1.Answer the following questions for $T_6$ distribution

a. $\mathbb{P}(T_6<1)$ and show the shaded area on the density plot. b. $\mathbb{P}(T_6>2)$ and show the shaded area on the density plot. c. $\mathbb{P}(-1