Getting unexpected output for state machine code

module mealy(input x_in,rst_n,clk, output reg y_out);

parameter s0 = 2'b00, s1 = 2'b01 , s2 = 2'b10;
reg [1:0] p_state,n_state;

always@(posedge clk,negedge rst_n) begin
    if(!rst_n) p_state <= s0;
    else
    p_state <= n_state;
end

always@(x_in,p_state) begin
    case (p_state)
        s0:
            n_state = x_in ? s2 : s1;
        s1: 
            n_state = x_in ? s2 : s1;
        s2:
            n_state = x_in ? s2 : s1;
    endcase
end

always@(x_in,p_state) begin
    case (p_state)
        s0:
            y_out = 1'b0;
        s1:
            y_out = x_in ? 1'b1 : 1'b0;
        s2:
            y_out = !x_in ? 1'b1 : 1'b0;
    endcase
end

endmodule

module mealy_tb;

reg x_in,rst_n,clk;
wire y_out;

mealy dut(x_in,rst_n,clk,y_out);

initial begin
    clk = 1'b0;
    forever #10 clk = ~clk;
end

initial begin
    rst_n = 1'b0;
    
    repeat(1000) begin
        x_in = {$random};
        rst_n = 1'b1;
        #10;
    end
    
end

endmodule

The state diagram is given below:

I am getting don't-care output. Also I am not able to view the state diagram in the state diagram viewer. I have specified the behaviour and output for each state. I am not able to find the error in the code. I need some guidance on writing code for state machines and also the reason why this code does not work?

You did not reset your design properly. Add a delay after setting rst_n to 0:

initial begin
    rst_n = 1'b0;
    #20;
    repeat(1000) begin
        x_in = {$random};
        rst_n = 1'b1;
        #10;
    end
    
end

The problem was easy to identify by viewing waveforms of your simulation. rst_n was always 1, which meant that p_state was always x (unknown).